Multiple Solutions of a p(x)-Laplacian Equation Involving Critical Nonlinearities

Authors

Yuan Liang, Zhejiang Wanli UniversityFollow
Xianbin Wu, Zhejiang Wanli University
Qihu Zhang, Zhengzhou University of Light Industry
Chunshan Zhao, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

12-2013

Publication Title

Taiwanese Journal of Mathematics

DOI

10.11650/tjm.17.2013.3074

ISSN

2224-6851

Abstract

In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions

−div(|∇u| p(x)−2 ∇u) + |u| ^p(x)−2 u = f(x, u) in Ω,

u = 0 on ∂Ω.

We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also present a variant of the concentration-compactness principle, which is of independent interest.

Comments

This is an open access article retrieved from the Taiwanese Journal of Mathematics.

Recommended Citation

Liang, Yuan, Xianbin Wu, Qihu Zhang, Chunshan Zhao. 2013. "Multiple Solutions of a p(x)-Laplacian Equation Involving Critical Nonlinearities." Taiwanese Journal of Mathematics, 17 (6): 2083-2100. doi: 10.11650/tjm.17.2013.3074
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/253