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

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.

36 pages

References in corpus (3)

• Fractional Quantum Mechanics
• On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity
• Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type nonlinearity

Cited by in corpus (1)

• Stationary solutions of a fractional Laplacian with singular perturbation