Localized nodal solutions for semiclassical Choquard equations

In this paper, we study the existence of localized nodal solutions for the semiclassical Choquard equation −ε2Δu+V(x)u=ε−α(Iα*|u|p)|u|p−2u for x∈RN. We establish for small ɛ the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function V by using the perturbation method and the method of invariant sets of descending flow.