High Energy Solutions to p(x)-Laplacian Equations of Schrödinger type

2012/10/19 by Duchao Liu, Xiaoyan Wang, Liu, Duchao +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1210.5308

21 pages

arxiv created 2012/10/19 · arxiv updated 2012/10/22

Abstract

In this paper, we investigate nonlinear Schrodinger type equations in R^N under the framework of variable exponent spaces. We propose new assumptions on the nonlinear term to yield bounded Palais-Smale sequences and then prove the special sequences we find converge to critical points respectively. The main arguments are based on the geometry supplied by Fountain Theorem. Consequently, we show that the equation has a sequence of solutions with high energies.

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