On the lack of bound states for certain NLS equations on metric graphs. (November 2016)

• Record Type: Journal Article
• Authors: Serra, Enrico; Tentarelli, Lorenzo
• Is Part Of: Nonlinear analysis. Volume 145(2016)
• Page Start: 68
• Page End: 82
• Publication Date: 2016-11
• Subjects: 35R02 -- 35Q55 -- 81Q35 -- 35Q40; Metric graphs -- NLS -- Localized nonlinearity -- Bound states; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.07.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The purpose of this paper is to prove some results on the absence of bound states for certain nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearity. In particular, we show how the topological and metric properties of graphs affect the existence/nonexistence of bound states. This work completes the discussion initiated in Serra and Tentarelli (2016) and Tentarelli (2016).