Semiclassical stationary states of nonlinear Schrodinger equations with an external magnetic field

In this paper we obtain multiple solutions u : R-N --> C of the nonlinear Schrodinger equation with an external magnetic field (h/idel - A(x))(2) u + (U(x)-E)u=f(x,u), xis an element ofR(N), where N greater than or equal to 2, A is a real-valued vector magnetic potential, U is a real electric potential function and the nonlinear term f (x, t) grows subcritically in t. The number of solutions to the equation is shown to be bounded below by some number which depends on the category of a set defined by some properties of V and the coefficients of the nonlinear term. We perform appropriate changes of gauges which are made on functions which are concentrated around points lying in some well-defined manifold. (C) 2002 Elsevier Science (USA). All rights reserved.