A new variational method for thep(x)-Laplacian equation

DOI10.1017/S0004972700034870zbMath1115.35035MaRDI QIDQ5694929

Marek Galewski

Publication date: 5 October 2005

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

elliptic equationsdual variational method

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear elliptic equations (35J60) Initial value problems for nonlinear first-order PDEs (35F25) Variational methods for second-order elliptic equations (35J20)

Related Items (18)

Existence of solutions for the \(p(x)\)-Laplacian problem with singular term ⋮ On a Dirichlet problem with \(p(x)\)-Laplacian ⋮ Solutions to p(x)-Laplace type equations via nonvariational techniques ⋮ On the existence and stability of solutions for Dirichlet problem with \(p(x)\)-Laplacian ⋮ Existence of solutions for the \(p(x)\)-Laplacian problem with the critical Sobolev-Hardy exponent ⋮ Nonlocal variational principles with variable growth ⋮ Existence of solutions for quasilinear elliptic systems in divergence form with variable growth ⋮ The Neumann boundary value problem of higher order quasilinear elliptic equation ⋮ Unnamed Item ⋮ On a Dirichlet Problem with Generalizedp(x)-Laplacian and Some Applications ⋮ Three solutions for a differential inclusion problem involving the \(p(x)\)-Laplacian ⋮ Infinitely many non-negative solutions for a Dirichlet problem involving \(p(x)\)-Laplacian ⋮ Infinitely many solutions for a Neumann-type differential inclusion problem involving the \(p(x)\)-Laplacian ⋮ Existence result for a gradient-type elliptic system involving a pair ofp(x) andq(x)-Laplacian operators ⋮ Three solutions for a Neumann-type differential inclusion problem involving the \(p(x)\)-Laplacian ⋮ Infinitely many solutions for a differential inclusion problem in \(\mathbb R^N\) involving the \(p(x)\)-Laplacian ⋮ On a nonlocal problem involving a nonstandard nonhomogeneous differential operator ⋮ The Dirichlet problem of higher order quasilinear elliptic equation

Cites Work

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• Electrorheological fluids: modeling and mathematical theory
• Existence results to elliptic systems with nonstandard growth conditions
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Some existence results for a class of nonlinear equations involving a duality mapping
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
• On the new variational principles and duality for periodic solutions of Lagrange equations with superlinear nonlinearities

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