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