On the existence of blowing-up solutions for a mean field equation
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 2, pp. 227-257.
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     title = {On the existence of blowing-up solutions for a mean field equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {227--257},
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     volume = {22},
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     zbl = {1129.35376},
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     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.001/}
}
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Esposito, Pierpaolo; Grossi, Massimo; Pistoia, Angela. On the existence of blowing-up solutions for a mean field equation. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 2, pp. 227-257. doi : 10.1016/j.anihpc.2004.12.001. https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.001/

[1] Ambrosetti A., Garcia Azorero J., Peral I., Perturbation of Δu+u(N+2)/(N-2)=0, the scalar curvature problem in RN, and related topics, J. Funct. Anal. 165 (1999) 117-149. | MR | Zbl

[2] Aubin T., Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, Berlin, 1998. | MR | Zbl

[3] Bahri A., Critical Point at Infinity in Some Variational Problems, Pitman Research Notes Math., vol. 182, Longman House, Harlow, 1989. | MR | Zbl

[4] Bandle C., Isoperimetric Inequalities and Applications, Pitman Monographs Studies Math., vol. 7, Pitman, 1980. | MR | Zbl

[5] Baraket S., Pacard F., Construction of singular limits for a semilinear elliptic equation in dimension 2, Calc. Var. Partial Differential Equations 6 (1998) 1-38. | MR | Zbl

[6] Bebernes J., Eberly D., Mathematical Problems from Combustion Theory, Springer, Berlin, 1989. | MR | Zbl

[7] Bianchi G., Egnell H., A note on the Sobolev inequality, J. Funct. Anal. 100 (1991) 18-24. | MR | Zbl

[8] Brezis H., Merle F., Uniform estimates and blow-up behavior for solutions of -Δu=Vx0ex0exeu in two dimensions, Comm. Partial Differential Equations 16 (1991) 1223-1253. | MR | Zbl

[9] Caglioti E., Lions P.L., Marchioro C., Pulvirenti M., A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description, Comm. Math. Phys. 143 (1992) 501-525. | MR | Zbl

[10] Caglioti E., Lions P.L., Marchioro C., Pulvirenti M., A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description. Part II, Comm. Math. Phys. 174 (1995) 229-260. | MR | Zbl

[11] Chae D., Imanuvilov O., The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys. 215 (2000) 119-142. | MR | Zbl

[12] D. Chae, G. Tarantello, On planar electroweak vortices, Ann. Inst. H. Poincaré Analyse Non Linéaire, in press.

[13] Chandrasekhar S., An Introduction to the Study of Stellar Structure, Dover, New York, 1957. | MR | Zbl

[14] Chen W., Li C., Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991) 615-623. | MR | Zbl

[15] Chen C.C., Lin C.S., Topological degree for a mean field equation on Riemann surfaces, Comm. Pure Appl. Math. 56 (2003) 1667-1727. | MR | Zbl

[16] Chen C.C., Lin C.S., On the simmetry of blowup solutions to a mean field equation, Ann. Inst. H. Poincaré Analyse Non Linéaire 18 (2001) 271-296. | Numdam | MR | Zbl

[17] M. Del Pino, M. Kowalczyk, M. Musso, Singular limits in Liouville-type equation, preprint. | MR

[18] Dancer E.N., On the uniqueness of the positive solution of a singularly perturbed problem, Rocky Mountain J. Math. 25 (1995) 957-975. | MR | Zbl

[19] Ding W., Jost J., Li J., Wang G., Existence results for mean field equations, Ann. Inst. H. Poincaré Analyse Non Linéaire 16 (1999) 653-666. | Numdam | MR | Zbl

[20] K. El Mehdi, M. Grossi, Asymptotic estimates and qualitative properties of an elliptic problem in dimension two, preprint. | MR

[21] P. Esposito, Blow up solutions for a Liouville equation with singular data, preprint, 2003. | MR

[22] P. Esposito, A class of Liouville-type equations arising in Chern-Simons vortex theory: asymptotics and construction of blowing up solutions, Thesis, Roma “Tor Vergata”, 2003.

[23] Gelfand I.M., Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl. 29 (1969) 295-381. | MR | Zbl

[24] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | MR | Zbl

[25] Grossi M., Pistoia A., On the effect of critical points of distance function in superlinear elliptic problems, Adv. Differential Equations 5 (2000) 1397-1420. | MR | Zbl

[26] Li Y.Y., On a singularly perturbed elliptic equation, Adv. Differential Equations 2 (1997) 955-980. | MR | Zbl

[27] Liouville J., Sur l’équation aud dérivées partielles 2logλ/uv±2λa2=0, J. Math. 18 (1853) 71-72.

[28] Ma L., Wei J., Convergence for a Liouville equation, Comment. Math. Helv. 76 (2001) 506-514. | MR | Zbl

[29] Mizoguchi N., Suzuki T., Equations of gas combustion: S-shaped bifurcation and mushrooms, J. Differential Equations 134 (1997) 183-215. | MR | Zbl

[30] Moseley J.L., Asymptotic solutions for a Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal. 14 (1983) 719-735. | MR | Zbl

[31] Moseley J.L., A two-dimensional Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal. 14 (1983) 934-946. | MR | Zbl

[32] Moser J., A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1970/71) 1077-1092. | MR | Zbl

[33] Musso M., Pistoia A., Multispike solutions for a nonlinear elliptic problem involving the critical Sobolev exponent, Indiana Univ. Math. J. 51 (2002) 541-579. | MR | Zbl

[34] Murrey J.D., Mathematical Biology, Springer, Berlin, 1989.

[35] Nagasaki K., Suzuki T., Asymptotic analysis for a two dimensional elliptic eigenvalue problem with exponentially dominated nonlinearity, Asymptotic Anal. 3 (1990) 173-188. | MR | Zbl

[36] Nolasco M., Non-topological N-vortex condensates for the self-dual Chern-Simons theory, Comm. Pure Appl. Math. 56 (2003) 1752-1780. | MR | Zbl

[37] Rey O., The role of Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990) 1-52. | MR | Zbl

[38] Suzuki T., Two dimensional Emden-Fowler equation with exponential nonlinearity, Nonlinear Diffusion Equations and their Equilibrium States 3 (1992) 493-512. | MR | Zbl

[39] Suzuki T., Global analysis for a two-dimensional eigenvalue problem with exponential nonlinearity, Ann. Inst. H. Poincaré Analyse Non Linéaire 9 (1992) 367-398. | Numdam | MR | Zbl

[40] Trudinger N.S., On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967) 473-483. | MR | Zbl

[41] Weston V.H., On the asymptotic solution of a partial differential equation with exponential nonlinearity, SIAM J. Math. Anal. 9 (1978) 1030-1053. | MR | Zbl

  • Constantineau, K.; García-Azpeitia, C.; García-Naranjo, L. C.; Lessard, J.-P. Determination of Stable Branches of Relative Equilibria of the N-Vortex Problem on the Sphere, Communications in Mathematical Physics, Volume 406 (2025) no. 2 | DOI:10.1007/s00220-024-05220-2
  • D’Aprile, Teresa; Wei, Juncheng; Zhang, Lei On the construction of non-simple blow-up solutions for the singular Liouville equation with a potential, Calculus of Variations and Partial Differential Equations, Volume 63 (2024) no. 3 | DOI:10.1007/s00526-024-02676-x
  • Figueroa, Pablo Bubbling solutions for mean field equations with variable intensities on compact Riemann surfaces, Journal d'Analyse Mathématique, Volume 152 (2024) no. 2, p. 507 | DOI:10.1007/s11854-023-0303-2
  • Gladiali, F.; Grossi, M. On the critical points of solutions of PDE in non-convex settings: The case of concentrating solutions, Journal of Functional Analysis, Volume 287 (2024) no. 11, p. 110620 | DOI:10.1016/j.jfa.2024.110620
  • Song, Qingcong; Hao, Xinan Positive solutions for nonlocal differential equations with concave and convex coefficients, Positivity, Volume 28 (2024) no. 5 | DOI:10.1007/s11117-024-01086-9
  • Hu, Zhengni; Bartsch, Thomas The Morse Property of Limit Functions Appearing in Mean Field Equations on Surfaces with Boundary, The Journal of Geometric Analysis, Volume 34 (2024) no. 7 | DOI:10.1007/s12220-024-01664-z
  • Figueroa, Pablo, 2023 | DOI:10.2139/ssrn.4354199
  • Gurzadyan, V. G.; Fimin, N. N.; Chechetkin, V. M. Cosmic voids and the kinetic analysis, Astronomy Astrophysics, Volume 672 (2023), p. A95 | DOI:10.1051/0004-6361/202346139
  • Li, Houwang; Wei, Juncheng; Zou, Wenming Uniqueness, multiplicity and nondegeneracy of positive solutions to the Lane-Emden problem, Journal de Mathématiques Pures et Appliquées, Volume 179 (2023), p. 1 | DOI:10.1016/j.matpur.2023.09.001
  • Figueroa, Pablo Sign-changing bubble tower solutions for sinh-Poisson type equations on pierced domains, Journal of Differential Equations, Volume 367 (2023), p. 494 | DOI:10.1016/j.jde.2023.05.013
  • Fimin, Nikolay Nikolaevich; Chechetkin, Valery Mihailovich Determinism of genesis of large-scale structures in astrophysics, Keldysh Institute Preprints (2023) no. 67, p. 1 | DOI:10.20948/prepr-2023-67
  • Heihoff, Frederic Two New Functional Inequalities and Their Application to the Eventual Smoothness of Solutions to a Chemotaxis-Navier–Stokes System with Rotational Flux, SIAM Journal on Mathematical Analysis, Volume 55 (2023) no. 6, p. 7113 | DOI:10.1137/22m1531178
  • Larbi, Lilia; Trabelsi, Nihed Singular Limit Solutions for a 4-dimensional Emden–Fowler System of Liouville Type in Some General Case, Taiwanese Journal of Mathematics, Volume 27 (2023) no. 2 | DOI:10.11650/tjm/221202
  • Martinazzi, Luca; Thizy, Pierre-Damien; Vétois, Jérôme Sign-changing blow-up for the Moser–Trudinger equation, Journal of Functional Analysis, Volume 282 (2022) no. 2, p. 109288 | DOI:10.1016/j.jfa.2021.109288
  • D’Aprile, Teresa Non-symmetric blowing-up solutions for a class of Liouville equations in the ball, Journal of Mathematical Physics, Volume 63 (2022) no. 2 | DOI:10.1063/5.0064197
  • BARAKET, Sami; CHETOUANE, Rima; MTIRI, Foued Singular limiting radial solutions for 4-dimensional elliptic problem involving exponentially dominated nonlinearity, Mathematical Reports, Volume 25(75) (2022) no. 1, p. 23 | DOI:10.59277/mrar.2023.25.75.1.23
  • Goodrich, Christopher; Lizama, Carlos Existence and monotonicity of nonlocal boundary value problems: the one-dimensional case, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 152 (2022) no. 1, p. 1 | DOI:10.1017/prm.2020.90
  • Figueroa, Pablo A note on a sinh-Poisson type equation with variable intensities on pierced domains, Asymptotic Analysis, Volume 122 (2021) no. 3-4, p. 327 | DOI:10.3233/asy-201620
  • Goodrich, Christopher S. Discrete Kirchhoff equations with sign-changing coefficients, Journal of Difference Equations and Applications, Volume 27 (2021) no. 5, p. 664 | DOI:10.1080/10236198.2021.1929945
  • Goodrich, Christopher S. Topological analysis of doubly nonlocal boundary value problems, Journal of Fixed Point Theory and Applications, Volume 23 (2021) no. 2 | DOI:10.1007/s11784-021-00865-1
  • Grossi, Massimo; Mancini, Gabriele; Naimen, Daisuke; Pistoia, Angela Bubbling nodal solutions for a large perturbation of the Moser–Trudinger equation on planar domains, Mathematische Annalen, Volume 380 (2021) no. 1-2, p. 643 | DOI:10.1007/s00208-020-01975-w
  • Goodrich, Christopher S. A topological approach to nonlocal elliptic partial differential equations on an annulus, Mathematische Nachrichten, Volume 294 (2021) no. 2, p. 286 | DOI:10.1002/mana.201900204
  • Gladiali, Francesca A monotonicity result under symmetry and Morse index constraints in the plane, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 151 (2021) no. 3, p. 885 | DOI:10.1017/prm.2020.43
  • DelaTorre, Azahara; Mancini, Gabriele; Pistoia, Angela Sign-Changing Solutions for the One-Dimensional Non-Local sinh-Poisson Equation, Advanced Nonlinear Studies, Volume 20 (2020) no. 4, p. 739 | DOI:10.1515/ans-2020-2103
  • Deng, Shengbing Existence of solutions for some weighted mean field equations in dimension N, Applied Mathematics Letters, Volume 100 (2020), p. 106010 | DOI:10.1016/j.aml.2019.106010
  • Goodrich, Christopher S.; Lyons, Benjamin Nonlocal difference equations with sign-changing coefficients, Applied Mathematics Letters, Volume 106 (2020), p. 106371 | DOI:10.1016/j.aml.2020.106371
  • Davila, Juan; Del Pino, Manuel; Musso, Monica; Wei, Juncheng Gluing Methods for Vortex Dynamics in Euler Flows, Archive for Rational Mechanics and Analysis, Volume 235 (2020) no. 3, p. 1467 | DOI:10.1007/s00205-019-01448-8
  • DelaTorre, Azahara; Hyder, Ali; Martinazzi, Luca; Sire, Yannick The nonlocal mean-field equation on an interval, Communications in Contemporary Mathematics, Volume 22 (2020) no. 05, p. 1950028 | DOI:10.1142/s0219199719500287
  • Bartolucci, Daniele; Wolansky, Gershon Maximal entropy solutions under prescribed mass and energy, Journal of Differential Equations, Volume 268 (2020) no. 11, p. 6646 | DOI:10.1016/j.jde.2019.11.040
  • Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data, Journal of Differential Equations, Volume 269 (2020) no. 3, p. 2057 | DOI:10.1016/j.jde.2020.01.030
  • D'Aprile, Teresa; Wei, Juncheng Bubbling solutions for the Liouville equation with a singular source: Non-simple blow-up, Journal of Functional Analysis, Volume 279 (2020) no. 6, p. 108605 | DOI:10.1016/j.jfa.2020.108605
  • Infante, Gennaro Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem, Mathematics, Volume 9 (2020) no. 1, p. 4 | DOI:10.3390/math9010004
  • Baraket, Sami; Bazarbacha, Imen; Chetouane, Rima Singular limit solutions for a 2-dimensional semilinear elliptic system of Liouville type in some general case adding singular sources (Part I), Nonlinear Analysis, Volume 196 (2020), p. 111799 | DOI:10.1016/j.na.2020.111799
  • Zhang, Yibin; Shi, Lei Concentrating solutions for a planar elliptic problem with large nonlinear exponent and Robin boundary condition, Advances in Nonlinear Analysis, Volume 8 (2019) no. 1, p. 1252 | DOI:10.1515/anona-2015-0153
  • Lee, Youngae; Lin, Chang-Shou; Yang, Wen Existence of bubbling solutions without mass concentration, Annales de l'Institut Fourier, Volume 69 (2019) no. 2, p. 895 | DOI:10.5802/aif.3261
  • Baraket, Sami; Chebbi, Souhail; Chorfi, Nejmeddine Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms, Boundary Value Problems, Volume 2019 (2019) no. 1 | DOI:10.1186/s13661-019-1244-7
  • Bartolucci, Daniele Global bifurcation analysis of mean field equations and the Onsager microcanonical description of two-dimensional turbulence, Calculus of Variations and Partial Differential Equations, Volume 58 (2019) no. 1 | DOI:10.1007/s00526-018-1445-4
  • Battaglia, Luca; Grossi, Massimo; Pistoia, Angela Non-uniqueness of blowing-up solutions to the Gelfand problem, Calculus of Variations and Partial Differential Equations, Volume 58 (2019) no. 5 | DOI:10.1007/s00526-019-1607-z
  • Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen Local uniqueness of m-bubbling sequences for the Gel’fand equation, Communications in Partial Differential Equations, Volume 44 (2019) no. 6, p. 447 | DOI:10.1080/03605302.2019.1581801
  • Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen Uniqueness of bubbling solutions of mean field equations, Journal de Mathématiques Pures et Appliquées, Volume 123 (2019), p. 78 | DOI:10.1016/j.matpur.2018.12.002
  • D'Aprile, Teresa Blow-up phenomena for the Liouville equation with a singular source of integer multiplicity, Journal of Differential Equations, Volume 266 (2019) no. 11, p. 7379 | DOI:10.1016/j.jde.2018.12.005
  • Infante, Gennaro Nonzero positive solutions of nonlocal elliptic systems with functional BCs, Journal of Elliptic and Parabolic Equations, Volume 5 (2019) no. 2, p. 493 | DOI:10.1007/s41808-019-00049-6
  • Lee, Youngae; Lin, Chang-Shou Uniqueness of bubbling solutions with collapsing singularities, Journal of Functional Analysis, Volume 277 (2019) no. 2, p. 522 | DOI:10.1016/j.jfa.2019.02.002
  • Kowalczyk, Michał; Pistoia, Angela; Vaira, Giusi Maximal solution of the Liouville equation in doubly connected domains, Journal of Functional Analysis, Volume 277 (2019) no. 9, p. 2997 | DOI:10.1016/j.jfa.2019.06.013
  • Battaglia, Luca Uniform bounds for solutions to elliptic problems on simply connected planar domains, Proceedings of the American Mathematical Society, Volume 147 (2019) no. 10, p. 4289 | DOI:10.1090/proc/14482
  • TRABELSI, Nihed Singular limit solutions for 2-dimensional elliptic system with sub-quadrtatic convection term, Acta Mathematica Scientia, Volume 38 (2018) no. 4, p. 1174 | DOI:10.1016/s0252-9602(18)30807-5
  • Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence, Archive for Rational Mechanics and Analysis, Volume 230 (2018) no. 1, p. 397 | DOI:10.1007/s00205-018-1248-y
  • KAVALLARIS, N. I.; RICCIARDI, T.; ZECCA, G. A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass, European Journal of Applied Mathematics, Volume 29 (2018) no. 3, p. 515 | DOI:10.1017/s0956792517000286
  • Figueroa, Pablo; Musso, Monica Bubbling solutions for Moser–Trudinger type equations on compact Riemann surfaces, Journal of Functional Analysis, Volume 275 (2018) no. 10, p. 2684 | DOI:10.1016/j.jfa.2018.08.016
  • Yang, Haitao; Zhang, Yibin Bubbling solutions for an anisotropic planar elliptic problem with exponential nonlinearity, Nonlinear Analysis, Volume 174 (2018), p. 141 | DOI:10.1016/j.na.2018.04.011
  • Kowalczyk, Michał; Pistoia, Angela; Rybka, Piotr; Vaira, Giusi Free boundary problems arising in the theory of maximal solutions of equations with exponential nonlinearities, Séminaire Laurent Schwartz — EDP et applications (2018), p. 1 | DOI:10.5802/slsedp.122
  • Ahmedou, Mohameden; Ben Ayed, Mohamed Theory of “Critical Points at Infinity” and a Resonant Singular Liouville-Type Equation, Advanced Nonlinear Studies, Volume 17 (2017) no. 1, p. 139 | DOI:10.1515/ans-2016-6016
  • Yang, Haitao; Zhang, Yibin Boundary bubbling solutions for a planar elliptic problem with exponential Neumann data, Discrete Continuous Dynamical Systems - A, Volume 37 (2017) no. 10, p. 5467 | DOI:10.3934/dcds.2017238
  • Pistoia, Angela; Ricciardi, Tonia Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents, Discrete Continuous Dynamical Systems - A, Volume 37 (2017) no. 11, p. 5651 | DOI:10.3934/dcds.2017245
  • Ahmedou, Mohameden; Ben Ayed, Mohamed; Lucia, Marcello On a resonant mean field type equation: A "critical point at Infinity" approach, Discrete Continuous Dynamical Systems - A, Volume 37 (2017) no. 4, p. 1789 | DOI:10.3934/dcds.2017075
  • Tarantello, Gabriella Blow-up analysis for a cosmic strings equation, Journal of Functional Analysis, Volume 272 (2017) no. 1, p. 255 | DOI:10.1016/j.jfa.2016.10.009
  • Ricciardi, Tonia; Zecca, Gabriella Minimal blow-up masses and existence of solutions for an asymmetric sinh-Poisson equation, Mathematische Nachrichten, Volume 290 (2017) no. 14-15, p. 2375 | DOI:10.1002/mana.201600215
  • De Marchis, F.; Ricciardi, T. Existence of stationary turbulent flows with variable positive vortex intensity, Nonlinear Analysis: Real World Applications, Volume 38 (2017), p. 222 | DOI:10.1016/j.nonrwa.2017.04.013
  • Ricciardi, Tonia; Zecca, Gabriella On the Blow-Up of Solutions to Liouville-Type Equations, Advanced Nonlinear Studies, Volume 16 (2016) no. 1, p. 75 | DOI:10.1515/ans-2015-5015
  • Agudelo, Oscar; Pistoia, Angela Boundary concentration phenomena for the higher-dimensional Keller–Segel system, Calculus of Variations and Partial Differential Equations, Volume 55 (2016) no. 6 | DOI:10.1007/s00526-016-1083-7
  • Ferreira, Lucas C. F.; Montenegro, Marcelo; Santos, Matheus C. Existence and symmetry for elliptic equations in ℝ n with arbitrary growth in the gradient, Journal d'Analyse Mathématique, Volume 130 (2016) no. 1, p. 1 | DOI:10.1007/s11854-016-0027-7
  • Musso, Monica; Pistoia, Angela; Wei, Juncheng New blow-up phenomena for SU(n+ 1) Toda system, Journal of Differential Equations, Volume 260 (2016) no. 7, p. 6232 | DOI:10.1016/j.jde.2015.12.036
  • Kuhl, Christian Equilibria for the N-vortex-problem in a general bounded domain, Journal of Mathematical Analysis and Applications, Volume 433 (2016) no. 2, p. 1531 | DOI:10.1016/j.jmaa.2015.08.055
  • Pistoia, Angela; Ricciardi, Tonia Concentrating solutions for a Liouville type equation with variable intensities in 2D-turbulence, Nonlinearity, Volume 29 (2016) no. 2, p. 271 | DOI:10.1088/0951-7715/29/2/271
  • Battaglia, Luca; Jevnikar, Aleks; Malchiodi, Andrea; Ruiz, David A general existence result for the Toda system on compact surfaces, Advances in Mathematics, Volume 285 (2015), p. 937 | DOI:10.1016/j.aim.2015.07.036
  • Jevnikar, Aleks; Kallel, Sadok; Malchiodi, Andrea A topological join construction and the Toda system on compact surfaces of arbitrary genus, Analysis PDE, Volume 8 (2015) no. 8, p. 1963 | DOI:10.2140/apde.2015.8.1963
  • Bartolucci, Daniele; De Marchis, Francesca Supercritical Mean Field Equations on Convex Domains and the Onsager’s Statistical Description of Two-Dimensional Turbulence, Archive for Rational Mechanics and Analysis, Volume 217 (2015) no. 2, p. 525 | DOI:10.1007/s00205-014-0836-8
  • del Pino, Manuel; Román, Carlos Large conformal metrics with prescribed sign-changing Gauss curvature, Calculus of Variations and Partial Differential Equations, Volume 54 (2015) no. 1, p. 763 | DOI:10.1007/s00526-014-0805-y
  • del Pino, Manuel; Esposito, Pierpaolo; Figueroa, Pablo; Musso, Monica Nontopological Condensates for the Self‐Dual Chern‐Simons‐Higgs Model, Communications on Pure and Applied Mathematics, Volume 68 (2015) no. 7, p. 1191 | DOI:10.1002/cpa.21548
  • Wang, Liping; Ye, Dong Concentrating solutions for an anisotropic elliptic problem with large exponent, Discrete Continuous Dynamical Systems - A, Volume 35 (2015) no. 8, p. 3771 | DOI:10.3934/dcds.2015.35.3771
  • Esposito, P.; Morlando, F. On a quasilinear mean field equation with an exponential nonlinearity, Journal de Mathématiques Pures et Appliquées, Volume 104 (2015) no. 2, p. 354 | DOI:10.1016/j.matpur.2015.03.001
  • Kuhl, Christian Symmetric equilibria for the N-vortex problem, Journal of Fixed Point Theory and Applications, Volume 17 (2015) no. 3, p. 597 | DOI:10.1007/s11784-015-0242-3
  • D'Aprile, Teresa Sign-changing blow-up solutions for Hénon type elliptic equations with exponential nonlinearity, Journal of Functional Analysis, Volume 268 (2015) no. 8, p. 2067 | DOI:10.1016/j.jfa.2015.02.009
  • Battaglia, Luca Existence and multiplicity result for the singular Toda system, Journal of Mathematical Analysis and Applications, Volume 424 (2015) no. 1, p. 49 | DOI:10.1016/j.jmaa.2014.10.081
  • Castro, Hernán Asymptotic estimates for the least energy solution of a planar semi-linear Neumann problem, Journal of Mathematical Analysis and Applications, Volume 428 (2015) no. 1, p. 258 | DOI:10.1016/j.jmaa.2015.03.031
  • Deng, Shengbing; Garrido, Danilo; Musso, Monica Multiple blow-up solutions for an exponential nonlinearity with potential in R2, Nonlinear Analysis: Theory, Methods Applications, Volume 119 (2015), p. 419 | DOI:10.1016/j.na.2014.10.034
  • Chen, Wenjing; Deng, Shengbing; Figueroa, Pablo Concentrating solutions for an exponential nonlinearity with Robin boundary condition, Nonlinear Analysis: Theory, Methods Applications, Volume 129 (2015), p. 294 | DOI:10.1016/j.na.2015.09.004
  • Deng, Shengbing; Musso, Monica Blow up solutions for a Liouville equation with Hénon term, Nonlinear Analysis: Theory, Methods Applications, Volume 129 (2015), p. 320 | DOI:10.1016/j.na.2015.09.018
  • Morlando, Fabrizio Singular limits in higher order Liouville-type equations, Nonlinear Differential Equations and Applications NoDEA, Volume 22 (2015) no. 6, p. 1545 | DOI:10.1007/s00030-015-0335-0
  • Deng, Shengbing; Musso, Monica Multiple blow-up solutions for an anisotropic Emden Fowler equation in R2, Nonlinearity, Volume 28 (2015) no. 6, p. 1761 | DOI:10.1088/0951-7715/28/6/1761
  • D'Aprile, Teresa; Pistoia, Angela; Ruiz, David A continuum of solutions for the SU(3) Toda System exhibiting partial blow-up: Figure 1., Proceedings of the London Mathematical Society, Volume 111 (2015) no. 4, p. 797 | DOI:10.1112/plms/pdv042
  • Bartsch, Thomas; Pistoia, Angela Critical Points of the N-vortex Hamiltonian in Bounded Planar Domains and Steady State Solutions of the Incompressible Euler Equations, SIAM Journal on Applied Mathematics, Volume 75 (2015) no. 2, p. 726 | DOI:10.1137/140981253
  • Figueroa, Pablo Singular limits for Liouville-type equations on the flat two-torus, Calculus of Variations and Partial Differential Equations, Volume 49 (2014) no. 1-2, p. 613 | DOI:10.1007/s00526-012-0594-0
  • Gladiali, Francesca; Grossi, Massimo; Ohtsuka, Hiroshi; Suzuki, Takashi Morse Indices of Multiple Blow-Up Solutions to the Two-Dimensional Gel'fand Problem, Communications in Partial Differential Equations, Volume 39 (2014) no. 11, p. 2028 | DOI:10.1080/03605302.2014.930485
  • Grossi, Massimo; Takahashi, Futoshi On the location of two blowup points on an annulus for the mean field equation, Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, p. 615 | DOI:10.1016/j.crma.2014.04.006
  • Ohtsuka, Hiroshi On some properties of mean fields of equilibrium vortices described by the Hamiltonian, Fluid Dynamics Research, Volume 46 (2014) no. 3, p. 031422 | DOI:10.1088/0169-5983/46/3/031422
  • Ao, Weiwei; Wang, Liping New concentration phenomena forSU(3)Toda system, Journal of Differential Equations, Volume 256 (2014) no. 4, p. 1548 | DOI:10.1016/j.jde.2013.11.006
  • Deng, Shengbing; Musso, Monica Bubbling solutions for an exponential nonlinearity inR2, Journal of Differential Equations, Volume 257 (2014) no. 7, p. 2259 | DOI:10.1016/j.jde.2014.05.034
  • Choi, Woocheol; Kim, Seunghyeok; Lee, Ki-Ahm Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian, Journal of Functional Analysis, Volume 266 (2014) no. 11, p. 6531 | DOI:10.1016/j.jfa.2014.02.029
  • Bartolucci, Daniele; Lin, Chang-Shou Existence and uniqueness for mean field equations on multiply connected domains at the critical parameter, Mathematische Annalen, Volume 359 (2014) no. 1-2, p. 1 | DOI:10.1007/s00208-013-0990-6
  • Esposito, Pierpaolo; Figueroa, Pablo Singular mean field equations on compact Riemann surfaces, Nonlinear Analysis: Theory, Methods Applications, Volume 111 (2014), p. 33 | DOI:10.1016/j.na.2014.08.006
  • Micheletti, Anna Maria; Pistoia, Angela Non Degeneracy of Critical Points of the Robin Function with Respect to Deformations of the Domain, Potential Analysis, Volume 40 (2014) no. 2, p. 103 | DOI:10.1007/s11118-013-9340-2
  • Ricciardi, Tonia; Zecca, Gabriella Mean field equations with probability measure in 2D-turbulence, Ricerche di Matematica, Volume 63 (2014) no. S1, p. 255 | DOI:10.1007/s11587-014-0208-6
  • Zhang, Yibin; Yang, Haitao Construction of Nodal Bubbling Solutions for the Weighted Sinh-Poisson Equation, Abstract and Applied Analysis, Volume 2013 (2013), p. 1 | DOI:10.1155/2013/873948
  • Lin, Chang-Shou; Yan, Shusen Existence of Bubbling Solutions for Chern–Simons Model on a Torus, Archive for Rational Mechanics and Analysis, Volume 207 (2013) no. 2, p. 353 | DOI:10.1007/s00205-012-0575-7
  • CHANG, YIBIN; YANG, HAITAO SINGULAR LIMITS FOR 2-DIMENSIONAL ELLIPTIC NEUMANN PROBLEM WITH EXPONENTIAL NONLINEARITY AND SINGULAR DATA, Communications in Contemporary Mathematics, Volume 15 (2013) no. 05, p. 1350024 | DOI:10.1142/s0219199713500247
  • D'aprile, Teresa Multiple Blow-Up Solutions for the Liouville Equation with Singular Data, Communications in Partial Differential Equations, Volume 38 (2013) no. 8, p. 1409 | DOI:10.1080/03605302.2013.799487
  • BARAKET, SAMI; OUNI, TAIEB SINGULAR LIMITS FOR 2-DIMENSIONAL ELLIPTIC PROBLEMS INVOLVING EXPONENTIAL NONLINEARITIES WITH SUB-QUADRATIC CONVECTION TERM, Glasgow Mathematical Journal, Volume 55 (2013) no. 3, p. 537 | DOI:10.1017/s0017089512000729
  • Chang, Yibin; Yang, Haitao Singular Limits in Liouville-Type Equations with Mixed Interior and Boundary Singular Sources, International Journal of Theoretical Physics, Volume 52 (2013) no. 6, p. 1925 | DOI:10.1007/s10773-012-1331-3
  • Baraket, Sami; Abid, Imed; Ouni, Taieb Singular limits solution for two-dimensional elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights, Annali di Matematica Pura ed Applicata, Volume 191 (2012) no. 4, p. 845 | DOI:10.1007/s10231-012-0281-y
  • Chang, Yibin; Yang, Haitao Multiple blowing-up and concentrating solutions for Liouville-type equations with singular sources under mixed boundary conditions, Boundary Value Problems, Volume 2012 (2012) no. 1 | DOI:10.1186/1687-2770-2012-33
  • del Pino, Manuel; Musso, Monica; Ruf, Bernhard Beyond the Trudinger-Moser supremum, Calculus of Variations and Partial Differential Equations, Volume 44 (2012) no. 3-4, p. 543 | DOI:10.1007/s00526-011-0444-5
  • Dávila, Juan; Wei, Juncheng Point Ruptures for a MEMS Equation with Fringing Field, Communications in Partial Differential Equations, Volume 37 (2012) no. 8, p. 1462 | DOI:10.1080/03605302.2012.679990
  • BARTOLUCCI, DANIELE STABLE AND UNSTABLE EQUILIBRIA OF UNIFORMLY ROTATING SELF-GRAVITATING CYLINDERS, International Journal of Modern Physics D, Volume 21 (2012) no. 13, p. 1250087 | DOI:10.1142/s0218271812500873
  • Dávila, Juan; Topp, Erwin Concentrating solutions of the Liouville equation with Robin boundary condition, Journal of Differential Equations, Volume 252 (2012) no. 3, p. 2648 | DOI:10.1016/j.jde.2011.09.036
  • Bartolucci, D.; Lin, C.S. Sharp existence results for mean field equations with singular data, Journal of Differential Equations, Volume 252 (2012) no. 7, p. 4115 | DOI:10.1016/j.jde.2011.12.014
  • Deng, Shengbing Mixed interior and boundary bubbling solutions for Neumann problem in R2, Journal of Differential Equations, Volume 253 (2012) no. 2, p. 727 | DOI:10.1016/j.jde.2012.04.012
  • Dancer, E. Norman; Hillman, Jonathan; Pistoia, Angela Deformation retracts to the fat diagonal and applications to the existence of peak solutions of nonlinear elliptic equations, Pacific Journal of Mathematics, Volume 256 (2012) no. 1, p. 67 | DOI:10.2140/pjm.2012.256.67
  • Baraket, Sami; Abid, Imed; Ouni, Taieb; Trabelsi, Nihed Singular limiting solutions for elliptic problem involving exponentially dominated nonlinearity and convection term, Boundary Value Problems, Volume 2011 (2011) no. 1 | DOI:10.1186/1687-2770-2011-10
  • BARAKET, SAMI; BEN OMRANE, INES; OUNI, TAIEB; TRABELSI, NIHED SINGULAR LIMITS FOR 2-DIMENSIONAL ELLIPTIC PROBLEM WITH EXPONENTIALLY DOMINATED NONLINEARITY AND SINGULAR DATA, Communications in Contemporary Mathematics, Volume 13 (2011) no. 04, p. 697 | DOI:10.1142/s0219199711004282
  • Bartolucci, Daniele; Lin, Chang‐Shou; Tarantello, Gabriella Uniqueness and symmetry results for solutions of a mean field equation on 𝕊2 via a new bubbling phenomenon, Communications on Pure and Applied Mathematics, Volume 64 (2011) no. 12, p. 1677 | DOI:10.1002/cpa.20385
  • Bartolucci, Daniele A “Sup + C Inf” inequality for Liouville-type equations with singular potentials, Mathematische Nachrichten, Volume 284 (2011) no. 13, p. 1639 | DOI:10.1002/mana.200810250
  • Baraket, Sami; Ben Omrane, Ines; Ouni, Taieb Singular limits for 2-dimensional elliptic problem involving exponential nonlinearity with nonlinear gradient term, Nonlinear Differential Equations and Applications NoDEA, Volume 18 (2011) no. 1, p. 59 | DOI:10.1007/s00030-010-0084-z
  • Wei, Long Changing-sign bubble solutions for an anisotropic sinh-Poisson equation, Nonlinear Differential Equations and Applications NoDEA, Volume 18 (2011) no. 6, p. 685 | DOI:10.1007/s00030-011-0113-6
  • del Pino, Manuel; Esposito, Pierpaolo; Musso, Monica Nondegeneracy of entire solutions of a singular Liouvillle equation, Proceedings of the American Mathematical Society, Volume 140 (2011) no. 2, p. 581 | DOI:10.1090/s0002-9939-2011-11134-1
  • Bartolucci, Daniele On the Classification of N-Points Concentrating Solutions for Mean Field Equations and the Symmetry Properties of the N-Vortex Singular Hamiltonian on the Unit Disk, Acta Applicandae Mathematicae, Volume 110 (2010) no. 1, p. 1 | DOI:10.1007/s10440-008-9376-2
  • Bartsch, Thomas; Pistoia, Angela; Weth, Tobias N-Vortex Equilibria for Ideal Fluids in Bounded Planar Domains and New Nodal Solutions of the sinh-Poisson and the Lane-Emden-Fowler Equations, Communications in Mathematical Physics, Volume 297 (2010) no. 3, p. 653 | DOI:10.1007/s00220-010-1053-4
  • del Pino, Manuel; Musso, Monica; Ruf, Bernhard New solutions for Trudinger–Moser critical equations in R2, Journal of Functional Analysis, Volume 258 (2010) no. 2, p. 421 | DOI:10.1016/j.jfa.2009.06.018
  • Grossi, Massimo; Takahashi, Futoshi Nonexistence of multi-bubble solutions to some elliptic equations on convex domains, Journal of Functional Analysis, Volume 259 (2010) no. 4, p. 904 | DOI:10.1016/j.jfa.2010.03.008
  • ZHANG, LEI ASYMPTOTIC BEHAVIOR OF BLOWUP SOLUTIONS FOR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY AND SINGULAR DATA, Communications in Contemporary Mathematics, Volume 11 (2009) no. 03, p. 395 | DOI:10.1142/s0219199709003417
  • Bartolucci, D.; Lin, C. S. Uniqueness Results for Mean Field Equations with Singular Data, Communications in Partial Differential Equations, Volume 34 (2009) no. 7, p. 676 | DOI:10.1080/03605300902910089
  • Tarantello, Gabriella On Some Elliptic Problems in the Study of Selfdual Chern-Simons Vortices, Geometric Analysis and PDEs, Volume 1977 (2009), p. 117 | DOI:10.1007/978-3-642-01674-5_4
  • Castro, Hernán Solutions with spikes at the boundary for a 2D nonlinear Neumann problem with large exponent, Journal of Differential Equations, Volume 246 (2009) no. 8, p. 2991 | DOI:10.1016/j.jde.2009.02.001
  • Wei, Juncheng; Ye, Dong; Zhou, Feng Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 25 (2008) no. 3, p. 425 | DOI:10.1016/j.anihpc.2007.02.001
  • Musso, Monica; Clapp, Mónica; Muñoz, Claudio Singular limits for the bi-Laplacian operator with exponential nonlinearity in R4, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 25 (2008) no. 5, p. 1015 | DOI:10.1016/j.anihpc.2007.09.002
  • Suzuki, Takashi; Takahashi, Futoshi Nonlinear Eigenvalue Problem with Quantization, Handbook of Differential Equations - Stationary Partial Differential Equations, Volume 5 (2008), p. 277 | DOI:10.1016/s1874-5733(08)80011-3
  • Grossi, Massimo Radial solutions for the Brezis–Nirenberg problem involving large nonlinearities, Journal of Functional Analysis, Volume 254 (2008) no. 12, p. 2995 | DOI:10.1016/j.jfa.2008.03.007
  • Dávila, Juan; Kowalczyk, Michał; Montenegro, Marcelo Critical points of the regular part of the harmonic Green function with Robin boundary condition, Journal of Functional Analysis, Volume 255 (2008) no. 5, p. 1057 | DOI:10.1016/j.jfa.2007.11.023
  • Baraket, Sami; Dammak, Makkia; Ouni, Taieb; Pacard, Frank Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 24 (2007) no. 6, p. 875 | DOI:10.1016/j.anihpc.2006.06.009
  • Bartolucci, Daniele; Montefusco, Eugenio Blow‐up analysis, existence and qualitative properties of solutions for the two‐dimensional Emden–Fowler equation with singular potential, Mathematical Methods in the Applied Sciences, Volume 30 (2007) no. 18, p. 2309 | DOI:10.1002/mma.887
  • Esposito, Pierpaolo; Musso, Monica; Pistoia, Angela On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity, Proceedings of the London Mathematical Society, Volume 94 (2007) no. 2, p. 497 | DOI:10.1112/plms/pdl020
  • del Pino, Manuel; Musso, Monica Chapter 3 Bubbling in nonlinear elliptic problems near criticality, Volume 3 (2006), p. 215 | DOI:10.1016/s1874-5733(06)80007-0
  • Dávila, Juan; Pino, Manuel del; Musso, Monica; Wei, Juncheng Singular Limits of a Two-Dimensional Boundary Value Problem Arising in Corrosion Modelling, Archive for Rational Mechanics and Analysis, Volume 182 (2006) no. 2, p. 181 | DOI:10.1007/s00205-006-0421-x
  • Wei, Juncheng; Ye, Dong; Zhou, Feng Bubbling solutions for an anisotropic Emden–Fowler equation, Calculus of Variations and Partial Differential Equations, Volume 28 (2006) no. 2, p. 217 | DOI:10.1007/s00526-006-0044-y
  • Wei, Juncheng; Ye, Dong; Zhou, Feng Bubbling solutions for an anisotropic Emden–Fowler equation, Comptes Rendus. Mathématique, Volume 343 (2006) no. 4, p. 253 | DOI:10.1016/j.crma.2006.05.017
  • Pistoia, Angela Concentrating Solutions for a Two-dimensional Elliptic Problem with Large Exponent in Nonlinearity, Free Boundary Problems, Volume 154 (2006), p. 351 | DOI:10.1007/978-3-7643-7719-9_34
  • Esposito, Pierpaolo; Pistoia, Angela; Wei, Juncheng Concentrating solutions for the Hénon equation in ℝ2, Journal d'Analyse Mathématique, Volume 100 (2006) no. 1, p. 249 | DOI:10.1007/bf02916763
  • Esposito, Pierpaolo; Musso, Monica; Pistoia, Angela Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent, Journal of Differential Equations, Volume 227 (2006) no. 1, p. 29 | DOI:10.1016/j.jde.2006.01.023
  • del Pino, Manuel; Muñoz, Claudio The two-dimensional Lazer–McKenna conjecture for an exponential nonlinearity, Journal of Differential Equations, Volume 231 (2006) no. 1, p. 108 | DOI:10.1016/j.jde.2006.07.003
  • del Pino, Manuel; Kowalczyk, Michał; Musso, Monica Variational reduction for Ginzburg–Landau vortices, Journal of Functional Analysis, Volume 239 (2006) no. 2, p. 497 | DOI:10.1016/j.jfa.2006.07.006
  • Bartolucci, Daniele; Montefusco, Eugenio On the shape of blow-up solutions to a mean field equation, Nonlinearity, Volume 19 (2006) no. 3, p. 611 | DOI:10.1088/0951-7715/19/3/005
  • Pino, Manuel del; Wei, Juncheng Collapsing steady states of the Keller–Segel system, Nonlinearity, Volume 19 (2006) no. 3, p. 661 | DOI:10.1088/0951-7715/19/3/007
  • Dávila, Juan; del Pino, Manuel; Musso, Monica Concentrating solutions in a two-dimensional elliptic problem with exponential Neumann data, Journal of Functional Analysis, Volume 227 (2005) no. 2, p. 430 | DOI:10.1016/j.jfa.2005.06.010

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