Title

Existence of Strong Solutions of a P(X) -Laplacian Dirichlet Problem without the Ambrosetti-Rabinowitz Condition

Document Type

Article

Publication Date

1-2015

Publication Title

Computers & Mathematics with Applications

DOI

10.1016/j.camwa.2014.10.022

Abstract

In this paper, we consider the existence of strong solutions of the following p(x)-Laplacian Dirichlet problem via critical point theory {−div(∣∇u∣p(x)−2∇u)=f(x,u), in Ω, / u=0, on ∂Ω.

We give a new growth condition, under which, we use a new method to check the Cerami compactness condition. Hence, we prove the existence of strong solutions of the problem as above without the growth condition of the well-known Ambrosetti–Rabinowitz type and also give some results about multiplicity of the solutions.

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