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.
Acknowledgements
The authors would like to thank the anonymous referees for their carefully reading this paper and their useful comments.
Notes
No potential conflict of interest was reported by the authors.