Electron. J. Diff. Equ., Vol. 2016 (2016), No. 166, pp. 1-11.

Critical quasilinear Schrodinger equation with sign-changing potential

Li-Li Wang, Zhi-Qing Han

Abstract:
We study the existence of nontrivial solutions for a class of quasilinear Schrodinger equations in R^N with critical nonlinearity, where the potential is allowed to change signs. The quasilinear equations are reduced to semilinear equations by using a change of variable. The geometric hypotheses of a mountain pass theorem without compactness conditions are satisfied so that the equation possesses a nontrivial solution.

Submitted December 24, 2014. Published June 28, 2016.
Math Subject Classifications: 35A01, 35A15, 35Q55.
Key Words: Quasilinear Schrodinger equation; critical growth; sign-changing potential; mountain pass theorem; (PS)c sequence.

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Li-Li Wang
School of Mathematical Sciences
Dalian University of Technology
116024 Dalian, China
email: lili_wang@aliyun.com
Zhi-Qing Han
School of Mathematical Sciences
Dalian University of Technology
116024 Dalian, China
email: hanzhiq@dlut.edu.cn

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