Existence of solutions for a class of elliptic systems in \(\mathbb R^{N}\) involving the \((p(x),q(x))\)-Laplacian

DOI10.1155/2008/612938zbMath1180.35212OpenAlexW2000430157WikidataQ59218163 ScholiaQ59218163MaRDI QIDQ949013

B. E. Eshmatov

Publication date: 16 October 2008

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2008/612938

zbMATH Keywords

variational approachnonlinear elliptic system\(p(x)\)-Laplacian

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Second-order elliptic systems (35J47) Quasilinear elliptic equations with (p)-Laplacian (35J92) Boundary value problems for second-order elliptic systems (35J57)

Related Items

Existence of solutions for nonlinear Schrödinger systems with periodic data perturbations ⋮ Existence, multiplicity and numerical examples for Schrödinger systems with nonstandard \(p(x)\)-growth conditions ⋮ Minimization of elliptic non-local functionals involving \(\vec{p}(\cdot)\)-Laplacian ⋮ Existence and multiplicity of solutions to a nonlocal elliptic PDE with variable exponent and nonlinear boundary conditions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Overview of differential equations with non-standard growth ⋮ EXISTENCE OF SOLUTIONS FOR CRITICAL SYSTEMS WITH VARIABLE EXPONENTS ⋮ Existence result for a gradient-type elliptic system involving a pair ofp(x) andq(x)-Laplacian operators

Cites Work

• A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
• Existence of positive solutions for elliptic systems with nonstandard \(p(x)\)-growth conditions via sub-supersolution method
• Uniqueness of solutions of the parabolic variational inequality with variable exponent of nonlinearity
• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
• Existence results to elliptic systems with nonstandard growth conditions
• Regularity results for stationary electro-rheological fluids
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Multiple positive solutions for semilinear elliptic systems with nonlinear boundary condition
• Existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in \(\mathbb R^N\)
• Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
• The Nehari manifold for systems of nonlinear elliptic equations
• Elliptic equations and systems with nonstandard growth conditions: existence, uniqueness and localization properties of solutions
• Solutions for \(p(x)\)-Laplacian Dirichlet problems with singular coefficients
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS
• Existence of Solutions for a Class of Problems in IR N Involving the p(x)-Laplacian
• Variable Exponent, Linear Growth Functionals in Image Restoration
• Existence and multiplicity of solutions for a Neumann problem involving the \(p(x)\)-Laplace operator
• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)