Infinitely many solutions for nonhomogeneous Choquard equations

Tao Wang,Hui Guo

doi:10.14232/ejqtde.2019.1.24

Abstract

Infinitely many solutions for nonhomogeneous Choquard equations

Highlights

We are concerned with the following nonhomogeneous nonlocal problem
As we know, there is no result on the existence of infinitely many solutions of (1.1) with f = 0
The proof of (i) makes use of the property of eigenvalues in H tending to infinity as in [17]

Summary

Introduction

We are concerned with the following nonhomogeneous nonlocal problem. −α where Γ denotes the Gamma function. As we know, there is no result on the existence of infinitely many solutions of (1.1) with f = 0. The main purpose of this paper is to consider the existence of infinitely many solutions. To state main results clearly, we consider the following equation which is related to (1.1). Due to the difference of the action space H considered, the results and methods for cases (V1) and (V2) may be different. The compactness of nonlocal term is critical in the proof of Theorem (ii). The proof of (i) makes use of the property of eigenvalues in H tending to infinity as in [17] This method does not work for the case (V2) because H does not have such a property.

Preliminaries

Proof of the main results