Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity-Reference-Cited by-同舟云学术

Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity

Published:2016-05-03 Issue:05 Volume:15 Page:699-729
ISSN:0219-5305
Container-title:Analysis and Applications
language:en
Short-container-title:Anal. Appl.

Author:

Cho Yonggeun¹,Fall Mouhamed M.²,Hajaiej Hichem³,Markowich Peter A.⁴,Trabelsi Saber⁴

Affiliation:

1. Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756, South Korea

2. African Institute for Mathematical Sciences of Senegal, AIMS-Senegal, KM 2, Route de Joal, B.P. 14 18. Mbour, Sénégal

3. Institute of Mathematical Sciences, New York University Shanghai, Shanghai 200120, P. R. China

4. Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia

Abstract

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219530516500056

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