Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 44, pp. 1-9.

Title: Existence and multiplicity of solutions for a differential
       inclusion problem involving the p(x)-Laplacian
       
Author: Guowei Dai (Northwest Normal Univ., Lanzhou, China)

Abstract:
 In this article we consider the differential inclusion
 $$\displaylines{
 -\hbox{div}(|\nabla u|^{p(x)-2}\nabla u)\in \partial F(x,u)
 \quad\hbox{in }\Omega,\cr
 u=0 \quad \hbox{on }\partial \Omega
 }$$
 which involves the $p(x)$-Laplacian.
 By applying  the nonsmooth Mountain Pass Theorem, we obtain at
 least one nontrivial solution; and by applying the
 symmetric Mountain Pass Theorem, we obtain k-pairs of
 nontrivial solutions in $W_{0}^{1,p(x)}(\Omega)$.
 
Submitted December 31, 2009. Published March 26, 2010.
Math Subject Classifications: 35J20, 35J70, 35R70.
Key Words: p(x)-Laplacian; nonsmooth mountain pass theorem;
           differential inclusion.