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

The existence and concentration behavior of a nodal solution are established for the equation −ε2Δu + V (x)u = f (u) in Ω, where Ω is a domain in RN, not necessarily bounded, V is a positive Hölder continuous function and f ∈ C1(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 .  2004 Elsevier Inc. All rights reserved