Multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields and critical frequency

In this paper, we are concerned with the existence and asymptotic behavior of standing wave solution psi(x,t)= e-(i lambda Et) of nonlinear Schrodinger equations with electromagnetic fields i partial derivative psi/partial derivative t = -(del + iA(x))(2)psi + lambda W(x)psi - f(|psi|(2))psi, (t,x) is an element of R x R-N,R- with E being a critical frequency in the sense that inf(x is an element of RN) W(x)=E. We show that if the zero set of W - E has several isolated connected components Omega(1),...., Omega(k) such that the interior of Omega(i) is not empty and partial derivative Omega(i) is smooth, then for lambda > 0 large there exists, for any non-empty subset J subset of (1,2,...,k), a standing wave solution which is trapped in a neighborhood of boolean OR(jeJ) Omega(j). (C) 2008 Elsevier Inc. All rights reserved.