Positive solutions for critical inhomogeneous elliptic problems in non-contractible domains

DOI10.1016/j.na.2008.01.024zbMath1155.35373OpenAlexW2007467791MaRDI QIDQ2518132

Haiyang He, Jianfu Yang

Publication date: 13 January 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.01.024

zbMATH Keywords

Palais-Smale conditionpositive solutionscritical Sobolev exponentsemilinear elliptic equationLjusternik-Schnirelman categoryinhomogeneous problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

Related Items

Existence of multiple solutions for a quasilinear Neumann problem with critical exponent, The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent, Multiple positive solutions to a class of quasi-linear elliptic equations involving critical Sobolev exponent, Three positive solutions for Dirichlet problems involving critical Sobolev exponent and sign-changing weight, Positive solutions for a critical elliptic problem involving singular nonlinearity, Critical growth elliptic problems involving Hardy-Littlewood-Sobolev critical exponent in non-contractible domains, Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent, Existence of multiple positive solutions for fractional Laplace problems with critical growth and sign-changing weight in non-contractible domains

Cites Work

• Unnamed Item
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• On a min-max procedure for the existence of a positive solution for certain scalar field equations in \({\mathbb{R}}^ N\)
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• Four positive solutions for the semilinear elliptic equation: \(-\Delta u+u=a(x) u^p +f(x)\) in \(\mathbb{R}^N\)
• Symmetry breaking in a bounded symmetry domain
• Multiple solutions for inhomogeneous critical semilinear elliptic problems
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Remarks on some quasilinear elliptic equations
• Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations