On the location and profile of spike-layer nodal solutions to nonlinear Schrodinger equations

The existence and concentration behavior of a nodal solution are established for the equation -epsilon(2)Deltau + V(x)u = f(u) in Omega, where Omega is a domain in R-N, not necessarily bounded, V is a positive Holder continuous function and f is an element of C-1 (R) is an odd function having subcritical and superlinear growth. Under additional local condition on V, it is proved that such a solution has just one positive and one negative peaks, which are located around local minima of V. (C) 2004 Elsevier Inc. All rights reserved.