Multiple positive solutions for Kirchhoff-Schrödinger-Poisson system with general singularity

Abstract

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.

Keywords

• Kirchhoff-Schrödinger-Poisson system
• general singularity
• multiple solutions
• variational method
• perturbation