Bound states of the NLS equation on metric graphs with localized nonlinearities

被引：30

作者：

Serra, Enrico ^{[1
]}

Tentarelli, Lorenzo ^{[1
]}

机构：

[1] Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 07期

关键词：

Minimax methods; Metric graphs; Nonlinear Schrodinger equation; Localized nonlinearity; Krasnosel'skii genus; CONCENTRATED NONLINEARITIES; SCHRODINGER-EQUATIONS; SPECTRAL STATISTICS; ORBITAL STABILITY; QUANTUM GRAPHS; WAVES;

D O I：

10.1016/j.jde.2015.12.030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the existence of multiple bound states of prescribed mass for the nonlinear Schrodinger equation on a noncompact metric graph. The main feature is that the nonlinearity is localized only in a compact part of the graph. Our main result states that for every integer , the equation possesses at least k solutions of prescribed mass, provided that the mass is large enough. These solutions arise as constrained critical points of the NLS energy functional. Estimates for the energy of the solutions are also established. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：5627 / 5644

页数：18

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