An existence result for singular fractional Kirchhoff-Schr\"{o}dinger-Poisson system

TL;DR

This paper proves the existence of multiple solutions for a fractional Kirchhoff-Schrödinger-Poisson system with singularities, using variational methods and Moser iteration to handle weak and strong singular cases.

Contribution

It establishes the existence of infinitely many solutions for weak singularities and at least one for strong singularities in the fractional Kirchhoff-Schrödinger-Poisson system, which is novel.

Findings

Existence of infinitely many solutions for $0<b3<1$

Existence of at least one solution for $b3>1$

Application of variational techniques and Moser iteration

Abstract

In this paper, we study the existence of infinitely many weak solutions to a fractional Kirchhoff-Schr\"{o}dinger-Poisson system involving the weak singularity, i.e. when $0<\gamma<1$. Further, we obtain the existence of a solution with the strong singularity, i.e. when $\gamma>1$. We employ variational techniques to prove the existence and multiplicity results. Moreover, a $L^{\infty}$ estimate is obtained by using the Moser iteration method.