Multiple positive solutions for Kirchhoff-Schr\xf6dinger-Poisson system with general singularity

Qi Zhang

doi:10.1186/s13661-017-0858-x

Abstract

In this paper, we consider the existence of multiple positive solutions for Kirchhoff-Schrödinger-Poisson system with the nonlinear term containing both general singularity and quasicritical nonlinearity. By combining the variational method with the perturbation method, we obtain the existence of two positive solutions with the parameter λ small enough. One of the solutions is the local minimum of the corresponding functional, and the other is the limit of the mountain pass type solution to the perturbation problem.

Highlights

1 Introduction and main results In this paper, we are interested in discussing the existence and multiple positive solutions to the following general singular Kirchhoff-Schrödinger-Poisson system:
In [ ], the authors obtained the existence of two positive solutions to with h(x) by using the variational method and the perturbation method
Motivated by the above reference, especially by [, ], and based on our work [ ], in this paper, we would like to continue to study the existence of multiple solutions to the general singular Kirchhoff-Schrödinger-Poisson system ( . )

Summary

Introduction

1 Introduction and main results In this paper, we are interested in discussing the existence and multiple positive solutions to the following general singular Kirchhoff-Schrödinger-Poisson system: ) with n = and g being critical term: g(s) = s and obtained two positive solutions to this problem. In [ ], the authors obtained the existence of two positive solutions to with h(x) by using the variational method and the perturbation method.

Results

Conclusion