Localized nodal solutions for semiclassical Choquard equations

In this paper, we study the existence of localized nodal solutions for the semiclassical Choquard equation -epsilon(2)delta u+V(x)u = epsilon(-alpha)(I-alpha*|u|(p))|u|(p-2)u for x epsilon R-N. We establish for small e 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. Published under an exclusive license by AIP Publishing.