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Advances in Mathematical Physics
Volume 2018 (2018), Article ID 3615085, 11 pages
https://doi.org/10.1155/2018/3615085
Research Article

Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth

1Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China
2Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
3Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092, China

Correspondence should be addressed to Kaimin Teng; moc.361@3102nimiakgnet

Received 12 September 2017; Revised 12 November 2017; Accepted 16 November 2017; Published 3 January 2018

Academic Editor: Ciprian G. Gal

Copyright © 2018 Quanqing Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the following generalized quasilinear Schrödinger equations with critical growth where , , is a even function, , and for all , where . Under some suitable conditions, we prove that the equation has a nontrivial solution by variational method.