Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 875-895.
@article{AIHPC_2007__24_6_875_0,
     author = {Baraket, Sami and Dammak, Makkia and Ouni, Taieb and Pacard, Frank},
     title = {Singular limits for a $4$-dimensional semilinear elliptic problem with exponential nonlinearity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {875--895},
     publisher = {Elsevier},
     volume = {24},
     number = {6},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.06.009},
     mrnumber = {2371110},
     zbl = {1132.35038},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.06.009/}
}
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Baraket, Sami; Dammak, Makkia; Ouni, Taieb; Pacard, Frank. Singular limits for a $4$-dimensional semilinear elliptic problem with exponential nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 875-895. doi : 10.1016/j.anihpc.2006.06.009. http://www.numdam.org/articles/10.1016/j.anihpc.2006.06.009/

[1] 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

[2] Chang S.Y.A., Yang P., Fourth order equations in conformal geometry, in: Global Analysis and Harmonic Analysis, (Marseille-Luminy, 1999), Smin. Congr., vol. 4, Soc. Math. France, Paris, 2000, pp. 155-165. | MR | Zbl

[3] Chang S.Y.A., Yang P., On a fourth order curvature invariant, in: Branson T. (Ed.), Spectral Problems in Geometry and Arithmetic, Contemporary Mathematics, vol. 237, Amer. Math. Soc., 1999, pp. 9-28. | MR | Zbl

[4] Del Pino M., Kowalczyk M., Musso M., Singular limits in Liouville type equations, Calc. Var. Partial Differential Equations 24 (1) (2005) 47-81. | MR | Zbl

[5] Esposito P., Grossi M., Pistoia A., On the existence of blowing-up solutions for a mean field equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2) (2005) 227-257. | Numdam | MR | Zbl

[6] Lin C.S., Wei J., Locating the peaks of solutions via the maximum principle. II. A local version of the method of moving planes, Comm. Pure Appl. Math. 56 (6) (2003) 784-809. | MR | Zbl

[7] Liouville J., Sur l’équation aux différences partielles 2 log λ uv±λ 2a 2 =0, J. Math. 18 (1853) 17-72.

[8] Lockhart R., Mcowen R., Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (3) (1985) 409-447. | Numdam | MR | Zbl

[9] Malchiodi A., Djadli Z., Existence of conformal metrics with constant Q-curvature, Preprint, math.AP/0410141, Ann. of Math., submitted for publication.

[10] Mazzeo R., Elliptic theory of edge operators I, Comm. Partial Differential Equations 16 (10) (1991) 1616-1664. | MR | Zbl

[11] Melrose R., The Atiyah-Patodi-Singer Index Theorem, Res. Notes in Math., vol. 4, A.K. Peters Ltd., Wellesley, MA, 1993. | Zbl

[12] Mignot F., Murat F., Puel J.P., Variation d'un point de retournement par rapport au domaine, Comm. Partial Differential Equations 4 (1979) 1263-1297. | MR | Zbl

[13] Pacard F., Rivière T., Linear and Nonlinear Aspects of Vortices: The Ginzburg Landau Model, Progress in Nonlinear Differential Equations, vol. 39, Birkhäuser, 2000. | MR | Zbl

[14] Suzuki T., Two-dimensional Emden-Fowler equation with exponential nonlinearity, in: Nonlinear Diffusion Equations and Their Equilibrium States, vol. 3, Birkhäuser, 1992, pp. 493-512. | Zbl

[15] G. Tarantello, On Chern-Simons Theory, in: H. Berestycki (Ed.), Nonlinear PDE's and Physical Modeling: Superfluidity, Superconductivity and Reactive Flows, Kluver Academic Publishers, in press. | Zbl

[16] Wente H.C., Counterexample to a conjecture of H. Hopf, Pacific J. Math. 121 (1986) 193-243. | MR | Zbl

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

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