Semiclassical ground states for quasilinear Schrodinger equations with three times growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Zhang, Hui¹  Zhang, Fubao² 

[1] Jinling Inst Technol, Dept Math, Nanjing 211169, Jiangsu, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

关键词: Quasilinear Schrodinger equation;    Concentration;    Nehari manifold;    Semi-classical state;   

DOI  :  10.1016/j.jmaa.2017.07.045

来源: Elsevier

【 摘 要 】

In this paper, we study the quasilinear Schrodinger equation -epsilon(2)Delta u + V(x)u - epsilon(2)u Delta(u(2)) = Q(x)u(3), u is an element of H-1(R-3), where epsilon > 0 is a parameter, V and Q are positive bounded functions. For the equation with three times growth, we establish the existence of ground states for epsilon small using the method of Nehari manifold. We also describe the concentration phenomena of ground states as epsilon -> 0. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free