Super-critical boundary bubbling in a semilinear Neumann problem
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 1, pp. 45-82.
@article{AIHPC_2005__22_1_45_0,
     author = {del Pino, Manuel and Musso, Monica and Pistoia, Angela},
     title = {Super-critical boundary bubbling in a semilinear {Neumann} problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {45--82},
     publisher = {Elsevier},
     volume = {22},
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     year = {2005},
     doi = {10.1016/j.anihpc.2004.05.001},
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     zbl = {02141611},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.05.001/}
}
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del Pino, Manuel; Musso, Monica; Pistoia, Angela. Super-critical boundary bubbling in a semilinear Neumann problem. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 1, pp. 45-82. doi : 10.1016/j.anihpc.2004.05.001. https://www.numdam.org/articles/10.1016/j.anihpc.2004.05.001/

[1] Adimurthi , Mancini G., The Neumann problem for elliptic equations with critical nonlinearity, A tribute in honour of G. Prodi, Scuola Norm. Sup. Pisa (1991) 9-25. | MR | Zbl

[2] Adimurthi , Mancini G., Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math. 456 (1994) 1-18. | EuDML | MR | Zbl

[3] Adimurthi , Mancini G., Yadava S.L., The role of the mean curvature in semilinear Neumann problem involving critical exponent, Comm. Partial Differential Equations 20 (3-4) (1995) 591-631. | MR | Zbl

[4] Adimurthi , Pacella F., Yadava S.L., Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Funct. Anal. 113 (1993) 318-350. | MR | Zbl

[5] Adimurthi , Pacella F., Yadava S.L., Characterization of concentration points and L-estimates for solutions of a semilinear Neumann problem involving the critical Sobolev exponent, Differential Integral Equations 8 (1) (1995) 41-68. | MR | Zbl

[6] Cao D., Noussair E.S., The effect of geometry of the domain boundary in an elliptic Neumann problem, Adv. Differential Equations 6 (8) (2001) 931-958. | MR | Zbl

[7] Dancer E.N., Yan S., Multipeak solutions for a singularly perturbed Neumann problem, Pacific J. Math. 189 (2) (1999) 241-262. | MR | Zbl

[8] Del Pino M., Dolbeault J., Musso M., “Bubble-tower” radial solutions in the slightly supercritical Brezis-Nirenberg problem, J. Differential Equations 193 (2) (2003) 280-306. | Zbl

[9] Del Pino M., Felmer P., Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting, Indiana Univ. Math. J. 48 (3) (1999) 883-898. | MR | Zbl

[10] Del Pino M., Felmer P., Musso M., Two-bubble solutions in the super-critical Bahri-Coron's problem, Calc. Var. PDE 16 (2) (2003) 113-145. | MR | Zbl

[11] Del Pino M., Felmer P., Wei J., On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal. 31 (1) (1999) 63-79. | MR | Zbl

[12] Fowler R.H., Further studies on Emden's and similar differential equations, Quart. J. Math. 2 (1931) 259-288. | Zbl

[13] Grossi M., A class of solutions for the Neumann problem -Δu+λu=u(N+2)/(N-2), Duke Math. J. 79 (2) (1995) 309-334. | MR | Zbl

[14] Grossi M., Pistoia A., Wei J., Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Calc. Var. Partial Differential Equations 11 (2) (2000) 143-175. | MR | Zbl

[15] Gui C., Multi-peak solutions for a semilinear Neumann problem, Duke Math. J. 84 (1996) 739-769. | MR | Zbl

[16] Gui C., Ghoussoub N., Multi-peak solutions for a semilinear Neumann problem involving the critical Sobolev exponent, Math. Z. 229 (3) (1998) 443-474. | MR | Zbl

[17] Gui C., Lin C.-S., Estimates for boundary-bubbling solutions to an elliptic Neumann problem, J. Reine Angew. Math. 546 (2002) 201-235. | MR | Zbl

[18] Gui C., Wei J., Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations 158 (1) (1999) 1-27. | MR | Zbl

[19] Kowalczyk M., Multiple spike layers in the shadow Gierer-Meinhardt system: existence of equilibria and the quasi-invariant manifold, Duke Math. J. 98 (1) (1999) 59-111. | MR | Zbl

[20] Li Y.Y., On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations 23 (3-4) (1998) 487-545. | MR | Zbl

[21] Li Y.Y., Prescribing scalar curvature on Sn and related problems, part I, J. Differential Equations 120 (1996) 541-597. | MR | Zbl

[22] Y.Y. Li, L. Zhang, Liouville and Harnack type theorems for semilinear elliptic equations, preprint.

[23] Lin C.-S., Locating the peaks of solutions via the maximum principle, I. The Neumann problem, Comm. Pure Appl. Math. 54 (2001) 1065-1095. | MR | Zbl

[24] Lin C.-S., Ni W.-M., Takagi I., Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations 72 (1988) 1-27. | MR | Zbl

[25] Ni W.-M., Takagi I., On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 44 (1991) 819-851. | MR | Zbl

[26] Ni W.-M., Takagi I., Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J 70 (1993) 247-281. | MR | Zbl

[27] Ni W.-M., B Pan X., Takagi I., Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J. 67 (1) (1992) 1-20. | MR | Zbl

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

[29] Rey O., Boundary effect for an elliptic Neumann problem with critical nonlinearity, Comm. in PDE 22 (1997) 1055-1139. | MR | Zbl

[30] Rey O., An elliptic Neumann problem with critical nonlinearity in three dimensional domains, Comm. Contemp. Math. 1 (1999) 405-449. | MR | Zbl

[31] O. Rey, J. Wei, Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity, part I: N=3, J. Funct. Anal., submitted for publication. | Zbl

[32] Wang X.J., Neumann problem of semilinear elliptic equations involving critical Sobolev exponent, J. Differential Equations 93 (1991) 283-301. | MR | Zbl

[33] Wang Z.Q., The effect of domain geometry on the number of positive solutions of Neumann problems with critical exponents, Differential Integral Equations 8 (1995) 1533-1554. | MR | Zbl

[34] Wei J., On the boundary spike layer solutions to a singularly perturbed Neumann problem, J. Differential Equations 134 (1) (1997) 104-133. | MR | Zbl

  • Chen, Lu; Lu, Guozhen; Zhang, Caifeng Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth, Calculus of Variations and Partial Differential Equations, Volume 63 (2024) no. 1 | DOI:10.1007/s00526-023-02621-4
  • Colasuonno, Francesca; Noris, Benedetta; Sovrano, Elisa Continuous dependence for p-Laplace equations with varying operators, Discrete and Continuous Dynamical Systems - S, Volume 0 (2024) no. 0, p. 0 | DOI:10.3934/dcdss.2024121
  • Cowan, Craig; Moameni, Abbas On supercritical elliptic problems: existence, multiplicity of positive and symmetry breaking solutions, Mathematische Annalen, Volume 389 (2024) no. 2, p. 1731 | DOI:10.1007/s00208-023-02685-9
  • Bonheure, Denis; Casteras, Jean-Baptiste; Premoselli, Bruno Classification of radial blow-up at the first critical exponent for the Lin–Ni–Takagi problem in the ball, Mathematische Annalen, Volume 390 (2024) no. 4, p. 5553 | DOI:10.1007/s00208-024-02888-8
  • Chen, Wenjing; Huang, Xiaomeng Sign-changing bubble tower solutions for a Paneitz-type problem, Nonlinearity, Volume 37 (2024) no. 5, p. 055013 | DOI:10.1088/1361-6544/ad36a3
  • Cowan, Craig Nonradial solutions of a Neumann Hénon equation on a ball, Proceedings of the American Mathematical Society (2024) | DOI:10.1090/proc/16897
  • Ben Ayed, Mohamed; El Mehdi, Khalil; Mohamed Salem, Fatimetou Interior Multi-Peak Solutions for a Slightly Subcritical Nonlinear Neumann Equation, Symmetry, Volume 16 (2024) no. 3, p. 291 | DOI:10.3390/sym16030291
  • Ben Ayed, Mohamed; El Mehdi, Khalil Nonexistence of interior bubbling solutions for slightly supercritical elliptic problems, Boundary Value Problems, Volume 2023 (2023) no. 1 | DOI:10.1186/s13661-023-01779-2
  • Pistoia, Angela; Saldaña, Alberto; Tavares, Hugo Existence of Solutions to a Slightly Supercritical Pure Neumann Problem, SIAM Journal on Mathematical Analysis, Volume 55 (2023) no. 4, p. 3844 | DOI:10.1137/22m1520360
  • Zhang, Yibin Boundary separated and clustered layer positive solutions for an elliptic Neumann problem with large exponent, Communications in Contemporary Mathematics, Volume 24 (2022) no. 10 | DOI:10.1142/s0219199721500887
  • Cowan, Craig; Moameni, Abbas Supercritical elliptic problems on nonradial domains via a nonsmooth variational approach, Journal of Differential Equations, Volume 341 (2022), p. 292 | DOI:10.1016/j.jde.2022.09.014
  • Cowan, C. Supercritical problems via a fixed point argument on the cone of monotonic functions, Nonlinear Differential Equations and Applications NoDEA, Volume 29 (2022) no. 6 | DOI:10.1007/s00030-022-00802-2
  • Casteras, Jean-Baptiste; Földes, Juraj Singular radial solutions for the Lin–Ni–Takagi equation, Calculus of Variations and Partial Differential Equations, Volume 59 (2020) no. 5 | DOI:10.1007/s00526-020-01824-3
  • Musso, Monica; Pimentel, Juliana A semilinear elliptic equation with competing powers and a radial potential, Journal d'Analyse Mathématique, Volume 140 (2020) no. 1, p. 283 | DOI:10.1007/s11854-020-0089-4
  • Moameni, Abbas Critical point theory on convex subsets with applications in differential equations and analysis, Journal de Mathématiques Pures et Appliquées, Volume 141 (2020), p. 266 | DOI:10.1016/j.matpur.2020.05.005
  • del Pino, Manuel; Musso, Monica; Román, Carlos; Wei, Juncheng Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3, Journal d'Analyse Mathématique, Volume 137 (2019) no. 2, p. 813 | DOI:10.1007/s11854-019-0008-8
  • Cowan, Craig; Moameni, Abbas A new variational principle, convexity, and supercritical Neumann problems, Transactions of the American Mathematical Society, Volume 371 (2019) no. 9, p. 5993 | DOI:10.1090/tran/7250
  • Manna, Bhakti B.; Pistoia, Angela Boundary-layers for a Neumann problem at higher critical exponents, Bollettino dell'Unione Matematica Italiana, Volume 10 (2017) no. 3, p. 355 | DOI:10.1007/s40574-016-0108-7
  • Dávila, Juan; Faya, Jorge; Mahmoudi, Fethi New type of solutions to a slightly subcritical Hénon type problem on general domains, Journal of Differential Equations, Volume 263 (2017) no. 11, p. 7221 | DOI:10.1016/j.jde.2017.08.005
  • Pistoia, Angela; Román, Carlos Large conformal metrics with prescribed scalar curvature, Journal of Differential Equations, Volume 263 (2017) no. 9, p. 5902 | DOI:10.1016/j.jde.2017.07.005
  • Chen, Wenjing Boundary bubbling solutions for a supercritical Neumann problem with mixed nonlinearities, Journal of Mathematical Analysis and Applications, Volume 454 (2017) no. 2, p. 759 | DOI:10.1016/j.jmaa.2017.05.005
  • Chen, Wenjing; Deng, Shengbing Sign-changing bubble tower solutions for a supercritical elliptic problem with the Hénon term, Nonlinearity, Volume 30 (2017) no. 12, p. 4344 | DOI:10.1088/1361-6544/aa870f
  • Musso, Monica; Mahmoudi, Fethi; Deng, Shengbing Bubbling on boundary submanifolds for a semilinear Neumann problem near high critical exponents, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 6, p. 3035 | DOI:10.3934/dcds.2016.36.3035
  • Chen, Wenjing; Guerra, Ignacio Multiplicity of solutions to nearly critical elliptic equation in the bounded domain of R3, Journal of Mathematical Analysis and Applications, Volume 424 (2015) no. 1, p. 179 | DOI:10.1016/j.jmaa.2014.11.019
  • Kuehn, Christian Infinite Dimensions, Multiple Time Scale Dynamics, Volume 191 (2015), p. 583 | DOI:10.1007/978-3-319-12316-5_18
  • Musso, Monica; Yang, Jun Curve-Like Concentration Layers for a Singularly Perturbed Nonlinear Problem with Critical Exponents, Communications in Partial Differential Equations, Volume 39 (2014) no. 6, p. 1048 | DOI:10.1080/03605302.2013.851215
  • Wang, Liping; Zhao, Chunyi Solutions with clustered bubbles and a boundary layer of an elliptic problem, Discrete Continuous Dynamical Systems - A, Volume 34 (2014) no. 5, p. 2333 | DOI:10.3934/dcds.2014.34.2333
  • Grossi, Massimo; Pistoia, Angela Multiple Blow-Up Phenomena for the Sinh-Poisson Equation, Archive for Rational Mechanics and Analysis, Volume 209 (2013) no. 1, p. 287 | DOI:10.1007/s00205-013-0625-9
  • Pistoia, Angela; Vétois, Jérôme Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds, Journal of Differential Equations, Volume 254 (2013) no. 11, p. 4245 | DOI:10.1016/j.jde.2013.02.017
  • Kim, Seunghyeok; Pistoia, Angela Boundary towers of layers for some supercritical problems, Journal of Differential Equations, Volume 255 (2013) no. 8, p. 2302 | DOI:10.1016/j.jde.2013.06.017
  • Weth, Tobias; Bonheure, Denis; Noris, Benedetta Increasing radial solutions for Neumann problems without growth restrictions, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 29 (2012) no. 4, p. 573 | DOI:10.1016/j.anihpc.2012.02.002
  • Pollack, Daniel; Pistoia, A.; Musso, Monica; Ge, Yuxin A refined result on sign changing solutions for a critical elliptic problem, Communications on Pure and Applied Analysis, Volume 12 (2012) no. 1, p. 125 | DOI:10.3934/cpaa.2013.12.125
  • Deng, Shengbing Multipeak solutions for asymptotically critical elliptic equations on Riemannian manifolds, Nonlinear Analysis: Theory, Methods Applications, Volume 74 (2011) no. 3, p. 859 | DOI:10.1016/j.na.2010.09.036
  • Ge, Yuxin; Musso, Monica; Pistoia, Angela Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains, Communications in Partial Differential Equations, Volume 35 (2010) no. 8, p. 1419 | DOI:10.1080/03605302.2010.490286
  • Musso, Monica; Pistoia, Angela Tower of bubbles for almost critical problems in general domains, Journal de Mathématiques Pures et Appliquées, Volume 93 (2010) no. 1, p. 1 | DOI:10.1016/j.matpur.2009.08.001
  • Allain, Geneviève; Beaulieu, Anne Singly periodic solutions of a semilinear equation, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 26 (2009) no. 4, p. 1277 | DOI:10.1016/j.anihpc.2008.10.001
  • Wei, Juncheng Existence and Stability of Spikes for the Gierer–Meinhardt System, Handbook of Differential Equations - Stationary Partial Differential Equations, Volume 5 (2008), p. 487 | DOI:10.1016/s1874-5733(08)80013-7
  • Campos, Juan F. “Bubble-Tower” phenomena in a semilinear elliptic equation with mixed Sobolev growth, Nonlinear Analysis: Theory, Methods Applications, Volume 68 (2008) no. 5, p. 1382 | DOI:10.1016/j.na.2006.12.032
  • Weth, Tobias; Pistoia, Angela Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 24 (2007) no. 2, p. 325 | DOI:10.1016/j.anihpc.2006.03.002
  • Lin, Changshou; Wang, Liping; Wei, Juncheng Bubble accumulations in an elliptic Neumann problem with critical Sobolev exponent, Calculus of Variations and Partial Differential Equations, Volume 30 (2007) no. 2, p. 153 | DOI:10.1007/s00526-006-0082-5
  • Wei, Juncheng; Yan, Shusen Lazer–McKenna conjecture: The critical case, Journal of Functional Analysis, Volume 244 (2007) no. 2, p. 639 | DOI:10.1016/j.jfa.2006.11.002
  • 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
  • Musso, Monica; Pistoia, Angela Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains☆☆The first author is supported by Fondecyt 1040936 (Chile). The second author is supported by the M.I.U.R. National Project “Metodi variazionali e topologici nello studio di fenomeni non lineari”., Journal de Mathématiques Pures et Appliquées, Volume 86 (2006) no. 6, p. 510 | DOI:10.1016/j.matpur.2006.10.006

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