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

TL;DR

This paper analyzes the orbital stability of standing waves in a class of nonlinear fractional Schrödinger equations with Hartree-type interactions, establishing existence, uniqueness, and stability results.

Contribution

It introduces a comprehensive analysis including existence, uniqueness, and orbital stability of standing waves for fractional Schrödinger equations with Hartree-type nonlinearities.

Findings

Existence and uniqueness of global solutions

Existence of standing waves via concentration-compactness

Orbital stability of the standing waves

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.