Variational and Stability Properties of Constant Solutions to the NLS Equation on Compact Metric Graphs

被引：0
作者：
Claudio Cacciapuoti
Simone Dovetta
Enrico Serra
机构：
[1] Università degli Studi dell’Insubria,Dipartimento di Scienza ed Alta Tecnologia
[2] Politecnico di Torino,Dipartimento di Scienze Matematiche “G.L. Lagrange”
来源：
Milan Journal of Mathematics | 2018年 / 86卷
关键词：
35R02; 35Q55; 49J40; 81Q35; Nonlinear Schrödinger equation; metric graphs; stationary solutions; critical growth; stability;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the nonlinear Schrödinger equation with pure power nonlinearity on a general compact metric graph, and in particular its stationary solutions with fixed mass. Since the the graph is compact, for every value of the mass there is a constant solution. Our scope is to analyze (in dependence of the mass) the variational properties of this solution, as a critical point of the energy functional: local and global minimality, and (orbital) stability. We consider both the subcritical regime and the critical one, in which the features of the graph become relevant. We describe how the above properties change according to the topology and the metric properties of the graph.
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页码：305 / 327
页数：22
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