Multiple solutions to a class of inclusion problem with the p(x)-Laplacian

Abstract

In this article, we obtain the existence of at least two nontrivial solutions for a nonlinear elliptic problem involving p(x)-Laplacian type operator and nonsmooth potentials. Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions.

Keywords:

• p(x)-Laplacian
• locally Lipschitz function
• variable exponent Sobolev space
• nonlinear eigenvalue problem
• multiple solutions

AMS Subject Classifications::

• 35R70
• 35J20
• 35J70

Acknowledgements

This article was supported by the National Science Fundation of China (No. 10971043, 11001063) and the Natural Natural Science Foundation of Hei Long Jiang Province (No. A200803).