Existence and multiplicity of solutions for a quasilinear Choquard equation via perturbation method

Abstract

In this paper, we consider the existence and multiplicity of solutions for the following quasilinear Choquard equation: −Δu+V(x)u−uΔ(u2)=(|x|−μ*|u|p)|u|p−2u,   x∈RN, where N ≥ 3, μ∈(0,N+22), p∈(2,4N−4μN−2). Under some assumptions on V, we obtain the existence of positive solutions, negative solutions, and high-energy solutions via perturbation method.