Multiple Solutions of a p(x)-Laplacian Equation Involving Critical NonlinearitiesTaiwanese Journal of Mathematics
AbstractIn 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 InformationYuan 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/