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

摘要

This article is concerned with the mathematical analysis of a class of anonlinear fractional Schrodinger equations with a general Hartree-typeintegrand. We prove existence and uniqueness of global-in-time solutions to theassociated Cauchy problem. Under suitable assumptions, we also prove theexistence of standing waves using the method of concentration-compactness bystudying the associated constrained minimization problem. Finally we show theorbital stability of standing waves which are the minimizers of the associatevariational problem.