Existence of infinitely many stationary solutions of the L2-subcritical and critical NLSE on compact metric graphs

被引：26

作者：

Dovetta, Simone ^{[1
,2
]}

机构：

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

[2] Univ Torino, Dipartimento Matemat G Peano, Via Carlo Alberto,10, I-10123 Turin, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 07期

关键词：

LOCALIZED NONLINEARITIES; STANDING WAVES; GROUND-STATES; BOUND-STATES; STAR GRAPHS; STABILITY; EQUATION; ENERGY;

D O I：

10.1016/j.jde.2017.12.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the existence of stationary solutions for the nonlinear Schrodinger equation on compact metric graphs. In the L-2-subcritical setting, we prove the existence of an infinite number of such solutions, for every value of the mass. In the critical regime, the existence of infinitely many solutions is established if the mass is lower than a threshold value, while global minimizers of the NLS energy exist if and only if the mass is lower or equal to the threshold. Moreover, the relation between this threshold and the topology of the graph is characterized. The investigation is based on variational techniques and some new versions of Gagliardo-Nirenberg inequalities. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：4806 / 4821

页数：16

共 38 条

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