Existence of solutions for p(x)-Laplacian dirichlet problem

Authors:
Xian-Ling Fan;Qi-Hu Zhang
Affiliations:
Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China;Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
Venue:
Nonlinear Analysis: Theory, Methods & Applications
Year:
2003

Citing 4
Cited 4

Nonlinear functional analysis and its applications

Nonlinear functional analysis and its applications
Regularity of nonstandard Lagrangians f(x, &xgr;)

Nonlinear Analysis: Theory, Methods & Applications
A class of De Giorgi type and Hölder continuity

Nonlinear Analysis: Theory, Methods & Applications
The quasi-minimizer of integral functionals with m(x) growth conditions

Nonlinear Analysis: Theory, Methods & Applications

Convergence Analysis for Incompressible Generalized Newtonian Fluid Flows with Nonstandard Anisotropic Growth Conditions

SIAM Journal on Numerical Analysis
Infinitely many homoclinic solutions for nonautonomous p(t)-Laplacian Hamiltonian systems

Computers & Mathematics with Applications
A pair of positive solutions for the Dirichlet p(z)-Laplacian with concave and convex nonlinearities

Journal of Global Optimization
Multiple critical points for non-differentiable parametrized functionals and applications to differential inclusions

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents several sufficient conditions for the existence of solutions for the Dirichlet problem of p(x)-Laplacian {-div(|∇u|p(x)-2∇u) = f(x,u), x ∈ Ω, u = 0, x ∈ ∂Ω. Especially, an existence criterion for infinite many pairs of solutions for the problem is obtained. The discussion is based on the theory of the spaces Lp(x)(Ω) and W01, p(x)(Ω).