Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains

DOI10.1016/S1631-073X(02)02614-6zbMath1032.35071MaRDI QIDQ1565924

Donato Passaseo, Riccardo Molle

Publication date: 27 May 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

critical pointsconcentration phenomenafinite dimensional reduction methodmini-max argumentmultispite solutions

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60)

Related Items

Positive solutions of slightly supercritical elliptic equations in symmetric domains, Multispike Solutions of Nonlinear Elliptic Equations with Critical Sobolev Exponent, Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains, Nonexistence of solutions for Dirichlet problems with supercritical growth in tubular domains, Nonexistence results for elliptic problems with supercritical growth in thin planar domains, Uniqueness of solutions for nonlinear Dirichlet problems with supercritical growth, Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical case, Multiple solutions of supercritical elliptic problems in perturbed domains, Concentration phenomena for solutions of superlinear elliptic problems, Nonlinear elliptic equations with large supercritical exponents

Cites Work

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• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains
• Multiplicity of positive solutions for the equation \(\Delta u + \lambda u + u^{2^*-1} =0\) in noncontractible domains
• On a variational problem with lack of compactness: The topological effect of the critical points at infinity
• Concentration phenomena in elliptic problems with critical and supercritical growth.
• Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Positive solutions of slightly supercritical elliptic equations in symmetric domains
• Some sufficient conditions for the existence of positive solutions to the equation \(-\Delta u + a(x)u = u^{2^* -1}\) in bounded domains
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• A multiplicity result for a variational problem with lack of compactness
• A Note on an Equation with Critical Exponent
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain