High energy solutions to p(x)-Laplacian equations of schrodinger type

In this article, we study nonlinear Schrodinger type equations in R^N under the framework of variable exponent spaces. We proposed new assumptions on the nonlinear term to yield bounded Palais-Smale sequences and then prove that the special sequences we found converge to critical points respectively...

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Published in:Electronic journal of differential equations 2015-05, Vol.2015 (136), p.1-17
Main Authors: Xiaoyan Wang, Jinghua Yao, Duchao Liu
Format: Article
Language:English
Subjects:
critical point
fountain theorem, Palais-Smale condition
p(x)-Laplacian
variable exponent Sobolev space
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Jinghua Yao
Duchao Liu
description In this article, we study nonlinear Schrodinger type equations in R^N under the framework of variable exponent spaces. We proposed new assumptions on the nonlinear term to yield bounded Palais-Smale sequences and then prove that the special sequences we found converge to critical points respectively. The main arguments are based on the geometry supplied by Fountain Theorem. Consequently, we showed that the equation under investigation admits a sequence of weak solutions with high energies.
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subjects critical point
fountain theorem, Palais-Smale condition
p(x)-Laplacian
variable exponent Sobolev space
title High energy solutions to p(x)-Laplacian equations of schrodinger type
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