INFINITELY MANY SOLUTIONS FOR A NONLINEAR SCHRODINGER EQUATION WITH NON-SYMMETRIC ELECTROMAGNETIC FIELDS

In this paper, we study the nonlinear Schrodinger equation with non-symmetric electromagnetic fields (del/i - A(epsilon)(x))(2)u + V-epsilon(x)u - f(u), u is an element of H-1 (R-N, C), where A(epsilon)(x) = (A(epsilon, 1)(x), A(epsilon, 2)(x), ... , A(epsilon, N)(x)) is a magnetic field satisfying that A(epsilon, j)(x)(j = 1, ... , N) is a real C-1 bounded function on R-N and V-epsilon(x) is an electric potential. Both of them satisfy some decay conditions but without any symmetric conditions and f (u) is a superlinear nonlinearity satisfying some non-degeneracy condition. Applying two times finite reduction methods and localized energy method, we prove that there exists some epsilon(0) > 0 such that for 0 < epsilon < epsilon(0), the above problem has infinitely many complex-valued solutions.