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.