An eigenvalue of an anisotropic quasilinear elliptic equation with variable exponent and Neumann boundary condition

DOI10.1016/j.na.2009.03.020zbMath1177.35074OpenAlexW2026042984MaRDI QIDQ838047

Chao Ji

Publication date: 21 August 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.2009.03.020

zbMATH Keywords

Neumann problemvariable exponent Sobolev spaceanisotropic quasilinear elliptic equation

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Variational methods for higher-order elliptic equations (35J35)

Related Items (14)

Local boundedness of quasi-minimizers of integral functionals with variable exponent anisotropic growth and applications ⋮ Minimization of elliptic non-local functionals involving \(\vec{p}(\cdot)\)-Laplacian ⋮ Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type ⋮ Unnamed Item ⋮ Generalized anisotropic Neumann problems of Ambrosetti-Prodi type with nonstandard growth conditions ⋮ The variational analysis of a nonlinear anisotropic problem with no-flux boundary condition ⋮ The number of solutions for a class of nonlocal nonhomogeneous gradient operator equations ⋮ On nonlocal \(\vec p (x)\)-Laplacian equations ⋮ Three weak solutions for a Neumann elliptic equations involving the \(\vec{p}(x)\)-Laplacian operator ⋮ On a class of anisotropic elliptic equations without Ambrosetti-Rabinowitz type conditions ⋮ Anisotropic variable exponent Sobolev spaces and -Laplacian equations ⋮ Multiplicity of solutions for a class of anisotropic elliptic equations with variable exponent ⋮ Multi-bump solutions for quasilinear elliptic equations with variable exponents and critical growth in ℝN ⋮ Some remarks on an eigenvalue problem for an anisotropic elliptic equation with indefinite weight

Cites Work

• Unnamed Item
• Electrorheological fluids: modeling and mathematical theory
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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