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.

Ground state solutions for a generalized quasilinear Choquard equation

“…When , a ground state solution was obtained in Chen et al, 14 and then, existence of positive solution of () was gained in Chen and Wu 15 by a variational argument. When , by using perturbation method, the existence of positive solutions, negative solutions, and high‐energy solutions were obtained in Yang et al 16 Yanget al 17 discussed the concentration behavior of ground states via dual approach. Zhang and Wu 18 considered a quasilinear Choquard equation with critical exponent and researched the existence, multiplicity, and concentration of positive solutions for the problem by a dual approach.…”

Ground state solutions for a class of quasilinear Choquard equation with critical growth

“…See for instance [1, 6, 9, 11, 14, 23-25, 27-30, 32], and the references therein. However, the problem (1.1) with Choquard type nonlinearity has only been studied in [2,7,8,33].…”

Nontrivial Solutions for a Class of Quasilinear Schrödinger Systems

“…In [9], for a type of quasilinear Schrödinger equation like (3), the author used the method developed by [10,11] to study ground state solutions. In addition, refs.…”