Infinitely many solutions for nonlinear Schrodinger equations with electromagnetic fields

In this paper, we study the nonlinear Schrodinger equation with electromagnetic fields (del/i - A(vertical bar y vertical bar))(2)u + V(vertical bar y vertical bar)u = vertical bar u vertical bar(p-1)u, u : R-N bar right arrow C, where the vector A(r) = (A(1)(r), A(2)(r), ... , A(N)(r)) is such that A(j)(r) (j = 1, 2, ... , N) is a real function on R+ and V(r) is a positive function on R+, 1 < p < N+2/N-2 if N >= 3 and 1 < p < +infinity if N = 2. We prove that the equation has infinitely many non-radial complex-valued solutions under conditions (H-1) and (H-2) which are given in Section 1. (C) 2011 Elsevier Inc. All rights reserved.