Nonlinear Schrödinger equation with growing potential on infinite metric graphs. (July 2019)

• Record Type: Journal Article
• Authors: Akduman, Setenay; Pankov, Alexander
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 258
• Page End: 272
• Publication Date: 2019-07
• Subjects: primary 35Q55 35R02 -- secondary 49J40 58E30; Metric graph -- Nonlinear Schrödinger equation -- Generalized Nehari manifold -- Bifurcation -- Exponential localization; 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.2019.02.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The paper deals with nonlinear Schrödinger equations on infinite metric graphs. We assume that the linear potential is infinitely growing. We prove an existence and multiplicity result that covers both self-focusing and defocusing cases. Furthermore, under some additional assumptions we show that solutions obtained bifurcate from trivial ones. We prove that these solutions are superexponentially localized. Our approach is variational and based on generalized Nehari manifold.