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Multiple Solutions of a p(x)-Laplacian Equation Involving Critical Nonlinearities
Taiwanese Journal of Mathematics
  • Yuan Liang, Zhejiang Wanli University
  • Xianbin Wu, Zhejiang Wanli University
  • Qihu Zhang, Zhengzhou University of Light Industry
  • Chunshan Zhao, Georgia Southern University
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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.


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

Citation Information
Yuan Liang, Xianbin Wu, Qihu Zhang and Chunshan Zhao. "Multiple Solutions of a p(x)-Laplacian Equation Involving Critical Nonlinearities" Taiwanese Journal of Mathematics Vol. 17 Iss. 6 (2013) p. 2083 - 2100 ISSN: 2224-6851
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