Multiplicity of solutions of the Dirichlet problem for an equation with the $p$-Laplacian in a three-dimensional spherical layer

DOI10.1090/S1061-0022-2011-01154-9zbMath1219.35116OpenAlexW2001831134MaRDI QIDQ3013554

S. B. Kolonitskii

Publication date: 18 July 2011

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2011-01154-9

zbMATH Keywords

\(p\)-Laplacianexistence of many solutions

Mathematics Subject Classification ID

Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (6)

The multiplicity of positive solutions to a quasilinear equation generated by the Il'in-Caffarelli-Cohn-Nirenberg inequality ⋮ Multiplicity of positive solutions for a critical quasilinear Neumann problem ⋮ Multiplicity of positive solutions to the boundary-value problems for fractional Laplacians ⋮ Second-order derivative of domain-dependent functionals along Nehari manifold trajectories ⋮ Multiplicity of solutions to the quasilinear Neumann problem in the 3-dimensional case ⋮ On qualitative properties of solutions for elliptic problems with thep-Laplacian through domain perturbations

Cites Work

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• The principle of symmetric criticality
• A nonlinear boundary value problem with many positive solutions
• Existence of many nonequivalent nonradial positive solutions of semilinear elliptic equations on three-dimensional annuli
• Existence of many positive solutions of semilinear equations on annulus
• On solutions to the Dirichlet problem for an equation with 𝑝-Laplacian in a spherical layer
• On harnack type inequalities and their application to quasilinear elliptic equations

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