\(p\)-Laplacian problems with critical Sobolev exponents

DOI10.1016/J.NA.2005.11.039zbMath1387.35254OpenAlexW1982724565MaRDI QIDQ858667

Elves A. B. Silva, Perera, Kanishka

Publication date: 11 January 2007

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.2005.11.039

zbMATH Keywords

variational methodscritical Sobolev exponentexistence and multiplicity\(p\)-Laplacian problems

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Critical exponents in context of PDEs (35B33) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (3)

The existence of positive solutions for the Neumann problem of \(p\)-Laplacian elliptic systems with Sobolev critical exponent ⋮ Existence of multiple solutions for singular elliptic problems with nonlinear boundary conditions ⋮ Multiple positive solutions for a critical quasilinear equation via Morse theory

Cites Work

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• The concentration-compactness principle in the calculus of variations. The limit case. II
• Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
• A note on the problem \(-\Delta u=\lambda u+u\,| u| ^{2^*-2}\)
• An existence result for nonliner elliptic problems involving critical Sobolev exponent
• Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
• A note on problems involving critical Sobolev exponents
• Multiplicity of positive solutions for some quasilinear elliptic equations in \(\mathbb{R}^N\) with critical Sobolev exponent
• Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations
• Quasilinear Dirichlet problems in \(\mathbb R^N\) with critical growth.
• Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
• \(p\)-Laplacian problems where the nonlinearity crosses an eigenvalue
• Quasilinear elliptic equations involving critical Sobolev exponents
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term
• A multiplicity result for quasilinear elliptic equations involving critical sobolev exponents
• Existence of positive solutions for m-Laplacian equations in N involving critical Sobolev exponents
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• On Critical Point Theory for Indefinite Functionals in The Presence of Symmetries

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