Semiclassical states for fractional Choquard equations with critical frequency

Abstract

ABSTRACTIn this paper, we study the semiclassical states for the fractional Choquard equation where , N>2s, , and , is a continuous potential satisfying suitable assumptions and is a small parameter. Using the mountain pass lemma and the Brezis-Lieb lemma, we prove the existence and asymptotic behavior of groundstates for and the nonexistence of solution for the minimization problem for , where Inspired by the result, we further consider the existence and asymptotic behavior of groundstates for the above equation under a nonlocal perturbation, that is, equation with .