ON MULTI-BUMP SEMI-CLASSICAL BOUND STATES OF NONLINEAR SCHRODINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS

We consider the existence and asymptotic behavior of standing wave solutions to nonlinear Schrodinger equations with electromagnetic fields: ih partial derivative psi/partial derivative t = (h/i del - A(x))(2) psi + W(x)psi - f(vertical bar psi vertical bar(2))psi on R x Omega. Omega subset of R-N is a domain which may be bounded or unbounded. For h > 0 small we obtain the existence of multi-bump bound states psi(h)(x, t) = e(-iEt/h)u(h)) where u(h) concentrates simultaneously at possibly degenerate, non-isolated local minima of W as h -> 0. We require that W >= E and allow the possibility that {x is an element of Omega : W(x) = E} not equal empty set. Moreover, we describe the asymptotic behavior of u(h) as h -> 0.