Ground states of nonlinear Schrodinger equation on star metric graphs

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Li, Yuhua¹  Li, Fuyi¹  Shi, Junping² 

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

关键词: Nonlinear Schrodinger equation;    Metric graph;    Star graph;    Variational method;    Ground state;   

DOI  :  10.1016/j.jmaa.2017.10.069

来源: Elsevier

【 摘 要 】

The existence and nonexistence of the ground state to nonlinear Schrodinger equation on several types of metric graphs are considered. In particular, for some star graphs with only one central vertex, the existence of ground state solution or positive solutions are shown. It is shown that the structure of the set of positive solution is quite different from the one for corresponding bounded n-dimensional domain. The proofs are based on variational methods, rearrangement arguments, energy estimates and phase plane analysis. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free