Orbital stability of standing waves of a class of fractional Schrodinger equations with a general Hartree-type integrand

2013/07/21 by Y. Cho, M. M. Fall, Cho, Y. +11 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1307.5523

36 pages

arxiv created 2013/07/21 · openalex publication_date 2013/07/21 · arxiv updated 2013/07/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This article is concerned with the mathematical analysis of a class of a nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We prove existence and uniqueness of global-in-time solutions to the associated Cauchy problem. Under suitable assumptions, we also prove the existence of standing waves using the method of concentration-compactness by studying the associated constrained minimization problem. Finally we show the orbital stability of standing waves which are the minimizers of the associate variational problem.

Citations

• Orbital stability of standing waves for some nonlinear Schr�dinger equations
• Regularity of the obstacle problem for a fractional power of the laplace operator
• On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity

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• Stationary solutions of a fractional Laplacian with singular\n perturbation

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