Xudong Shang, Zhigang Wang
Abstract:
In this article, we study the existence of solutions to
the problem
where
is a smooth bounded domain in
,
is a continuous function with
and
.
Applying nonsmooth critical point theory for locally Lipschitz functionals,
we show that there is at least one nontrivial solution when
less than a certain number, and
maybe discontinuous.
Submitted November 7, 2011. Published February 7, 2012.
Math Subject Classifications: 35J92, 35J70, 35R70
Key Words: p(x)-Laplacian problem; critical Sobolev exponents;
discontinuous nonlinearities.
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Xudong Shang School of Mathematics Nanjing Normal University Taizhou College 225300, Jiangsu, China email: xudong-shang@163.com | |
Zhigang Wang School of Mathematics Nanjing Normal University Taizhou College 225300, Jiangsu, China email: wzg19.scut@163.com |
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