Existence of non-trivial solutions for nonlinear fractional Schr\"{o}dinger-Poisson equations

TL;DR

This paper proves the existence of non-trivial solutions for a nonlinear fractional Schrödinger-Poisson equation in three-dimensional space using perturbation methods and the mountain pass theorem.

Contribution

It introduces a novel application of the mountain pass theorem to fractional Schrödinger-Poisson equations, establishing existence results in unbounded domains.

Findings

Existence of non-trivial solutions proven

Application of mountain pass theorem to fractional equations

Use of perturbation method in unbounded domain

Abstract

We prove the existence of non-trivial solutions for a fractional Schr$\ddot{o}$dinger-Poisson equation in $\mathbb{R}^{3}$. The proof is based on the perturbation method and the mountain pass theorem.