Inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity on the upper half-plane. (October 2019)

• Record Type: Journal Article
• Authors: Hayashi, Nakao; Kaikina, Elena I.
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 279
• Page End: 306
• Publication Date: 2019-10
• Subjects: 35Q35; Nonlinear Schrödinger equation -- Large time asymptotics -- Inhomogeneous initial–boundary value problem -- Upper half plane; 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.2019.05.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity in the upper half plane. We present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to the problem by using the classical energy method and factorization techniques.