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Article
Multiple Solutions of a p(x)-Laplacian Equation Involving Critical Nonlinearities
Taiwanese Journal of Mathematics
  • Yuan Liang
  • Xianbin Wu
  • Qihu Zhang
  • Chunshan Zhao, Georgia Southern University
Document Type
Article
Publication Date
12-1-2013
Disciplines
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.
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
Available at: http://works.bepress.com/chunshan_zhao/12/