Electron. J. Diff. Equ., Vol. 2015 (2015), No. 136, pp. 1-17.

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

Xiaoyan Wang, Jinghua Yao, Duchao Liu

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.

Submitted October 13, 2013. Published May 15, 2015.
Math Subject Classifications: 34D05, 35J20, 35J70.
Key Words: p(x)-Laplacian; variable exponent Sobolev space; critical point; fountain theorem, Palais-Smale condition.

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Xiaoyan Wang
Department of Mathematics
Indiana University
Bloomington, IN 47405, USA
email: wang264@indiana.edu
Jinghua Yao
Department of Mathematics
The University of Iowa
Iowa City, IA 52246, USA
email: jinghua-yao@uiowa.edu
Duchao Liu
Department of Mathematics
Lanzhou University
Lanzhou 730000, China
email: liuduchao@gmail.com, liudch@lzu.edu.cn

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