Existence and multiplicity of solutions for a class of generalized quasilinear Schrodinger equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Shi, Hongxia¹  Chen, Haibo¹ 

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

关键词: Quasilinear Schrodinger equations;    Standing wave solutions;    Variational methods;   

DOI  :  10.1016/j.jmaa.2017.03.020

来源: Elsevier

【 摘 要 】

This paper focuses on the following generalized quasilinear Schrodinger equations -div(g(2)(u)del u) + g(u)g'(u)vertical bar del u vertical bar(2) +V(x)u = f (x, u), x is an element of R-N, where N >= 3, g(s) : R -> R+ is a nondecreasing function with respect to vertical bar s vertical bar. By using a change of variables and variational methods, we obtain the existence and multiplicity of nontrivial solutions for the above problem when the nonlinearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free