Abstract
The purpose of this paper is to study the singular problem involving the p(x)-Laplace operator:
(Section.Display)
where
be a bounded domain with
boundary,
is a positive parameter and p(x),
and f(x, u) are assumed to satisfy the assumptions (H0)-(H4) in the Introduction. We employ variational techniques in order to show the existence of a number
such that problem
has two solutions for
one solution for
and no solutions for
To obtain multiple (at least two distinct, positive) solutions of problem
, we need to prove two new results: a regularity result for solutions to problem
in
with some
and a strong comparison principle.