Ground-states for systems of M coupled semilinear Schrödinger equations with attraction–repulsion effects: Characterization and perturbation results. (July 2016)

• Record Type: Journal Article
• Authors: Correia, Simão
• Is Part Of: Nonlinear analysis. Volume 140(2016)
• Page Start: 112
• Page End: 129
• Publication Date: 2016-07
• Subjects: 35Q55 -- 35J47 -- 35E99; Coupled semilinear Schrödinger equations -- Ground-states -- Nontrivial solutions -- Perturbations; 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.2016.03.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We focus on the study of ground-states for the system of M coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. We extend the characterization result in Correia (2016) to the case where both attraction and repulsion are present and cannot be studied separately. Furthermore, we derive some perturbation and classification results to study the general system where components may be out of phase. In particular, we present several conditions to the existence of nontrivial ground-states.