Standing waves of nonlinear Schrodinger equations with the gauge field

Abstract

We study standing waves for nonlinear Schrodinger equations with the gauge field. Some existence results of standing waves are established by applying variational methods to the functional which is obtained by representing the gauge field A(mu) in terms of complex scalar field phi. We also show that there exists no standing wave for certain range of parameters by establishing a new inequality of Sobolev type. (C) 2012 Elsevier Inc. All rights reserved.