Abstract
The purpose of this paper is to study the following nonlinear problem involving the p(x)-Laplace operator:
where
is a bounded domain with
boundary,
is a positive parameter, p(x), and f(x, u) are assumed to satisfy the assumptions (H1)-(H4) in the introduction. We employ variational techniques in order to show the existence of a number
such that problem
admits two solutions for
one solution for
and no solutions for