Concentration of solutions to elliptic equations with critical nonlinearity

DOI10.1016/S0294-1449(16)30245-1zbMath0761.35034OpenAlexW4386129333MaRDI QIDQ1199280

Olivier Rey

Publication date: 16 January 1993

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1992__9_2_201_0

zbMATH Keywords

existence of solutionsDirichlet boundary conditionsblow-uplimiting Sobolev exponentvariational problems with lack of compactness

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

Related Items (10)

Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian ⋮ Existence of solutions for a coupled Schrödinger equations with critical exponent ⋮ Multiplicity of positive solutions for semilinear elliptic equations involving the critical sobolev exponents ⋮ A prescribed scalar curvature-type equation: Almost critical manifolds and multiple solutions. ⋮ Multiple existence of solutions for a nonhomogeneous elliptic problem with critical exponent on \(\mathbb R^N\) ⋮ On nonhomogeneous elliptic equations involving critical Sobolev exponent ⋮ Sign-changing blowing-up solutions for a non-homogeneous elliptic equation at the critical exponent ⋮ Multiple positive solutions of nonhomogeneous equations involving the \(p\)-Laplacian ⋮ Concentration and multiplicity of solutions for a fourth-order equation with critical nonlinearity ⋮ MULTIPLE SOLUTIONS OF NONHOMOGENEOUS ELLIPTIC EQUATIONS WITH CRITICAL NONLINEARITY ON SYMMETRIC DOMAINS

Cites Work

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• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• A multiplicity result for a variational problem with lack of compactness
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain

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