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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Serra, Enrico¹  Tentarelli, Lorenzo¹ 

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

关键词: Minimax methods;    Metric graphs;    Nonlinear Schrodinger equation;    Localized nonlinearity;    Krasnosel'skii genus;   

DOI  :  10.1016/j.jde.2015.12.030

来源: Elsevier

【 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.

【 授权许可】

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