Some existence and concentration results for nonlinear Schrödinger equations

In this paper we are concerned with the existence of solutions with non-vanishing angular momentum for a class of nonlinear Schrödinger equations of the form where , , and the potential satisfies some symmetric properties. In particular the cases with radially symmetric and with having a cylindrical symmetry are discussed. Our main purpose is to study the asymptotic behaviour of such solutions in the semiclassical limit (i.e. as ) when a concentration phenomenon around a point of appears