Solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions

DOI10.1007/BF02567912zbMath0717.35029MaRDI QIDQ2638431

Mariette C. Knaap, Myriam Comte

Publication date: 1990

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155545

zbMATH Keywords

critical Sobolev exponentNeumann probleminfinitely many nontrivial solutions

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30)

Related Items (12)

On the least-energy solutions of the pure Neumann Lane-Emden equation ⋮ Positive solution for neumann problem with critical non linearity on boundary ⋮ Solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions ⋮ Existence of Solutions to a Slightly Supercritical Pure Neumann Problem ⋮ Positive solutions for elliptic equations involving critical Sobolev exponents and Hardy terms with Neumann boundary conditions. ⋮ On semilinear Neumann problems with critical growth for the n-Laplacian ⋮ A note on the positive energy solutions for elliptic equations involving critical Sobolev exponents ⋮ On the nonhomogeneous Neumann problem with weight and with critical nonlinearity in the boundary ⋮ Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents ⋮ Singular limit of quasilinear Neumann problems ⋮ On the Neumann problem for an elliptic system with weights and multiple critical nonlinearities ⋮ On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space

Cites Work

• Existence of a nonradial positive solution for the critical exponent problem with Neumann boundary condition
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• Critical Sobolev exponent problem in \({\mathbb{R}{}}^ n(n{\geq{}}4)\) with Neumann boundary condition
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• Solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Asymptotic behaviour of solutions of elliptic equations with critical exponents and Neumann boundary conditions
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