Electron. J. Differential Equations, Vol. 2020 (2020), No. 56, pp. 1-17.

Positive solutions for asymptotically 3-linear quasilinear Schrodinger equations

Guofa Li, Bitao Cheng, Yisheng Huang

Abstract:
In this article, we study the quasilinear Schrodinger equation

where $N\geq3$, $\kappa>0$ is a parameter, $V: \mathbb{R}^N\to\mathbb{R}$ is a given potential. The nonlinearity $h\in C(\mathbb{R}, \mathbb{R})$ is asymptotically 3-linear at infinity. We obtain the nonexistence of a least energy solution and the existence of a positive solution, via the Pohozaev manifold and a linking theorem. Our results improve recent results in [4, 22].

Submitted June 16, 2019. Published June 4, 2020.
Math Subject Classifications: 35J20, 35J62.
Key Words: Quasilinear Schrodinger equations; asymptotically 3-linear; Pohozaev identity; linking theorem; positive solution.
DOI: 10.58997/ejde.2020.56

Show me the PDF file (378 KB), TEX file for this article.

Guofa Li
College of Mathematics and Statistics
Qujing Normal University
Qujing 655011, China
email liguofa2013@163.com
Bitao Cheng
College of Mathematics and Statistics
Qujing Normal University
Qujing 655011, China
email: chengbitao2006@126.com
Yisheng Huang
Department of Mathematics
Soochow University
Suzhou 215006, China
email: yishengh@suda.edu.cn

Return to the EJDE web page