MULTIPLE SOLUTIONS OF A p(x)-LAPLACIAN EQUATION INVOLVING CRITICAL NONLINEARITIES
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چکیده
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.
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تاریخ انتشار 2013