An existence and stability result for standing waves of nonlinear Schrödinger equations

Abstract

We consider a nonlinear Schrödinger equation with a nonlinearity of the form V (x)g(u). Assuming that V (x) behaves like |x|-b at infinity and g(s) like |s|p around 0, we prove the existence and orbital stability of travelling waves if 1 < p < 1 + (4-2b)/N.