Two nontrivial solutions for a nonhomogeneous fractional Schrödinger–Poisson equation in $\mathbb{R}^{3}$

Abstract

In this paper, we consider the following nonhomogeneous fractional Schrödinger-Poisson equations:where s, t ∈ (0, 1], 2t + 4s > 3, (-) s denotes the fractional Laplacian. By assuming more relaxed conditions on the nonlinear term f , using some new proof techniques on the verification of the boundedness of Palais-Smale sequence, existence and multiplicity of solutions are obtained.

The nontrivial solutions for nonlinear fractional Schrödinger-Poisson system involving new fractional operator

“…For more details on the physics aspects, we refer the interested readers to [5,6,9] and their references. In recent years, several results and works have been published for fractional Schrödinger-Poisson systems on the multiplicity of solutions, the existence of ground state solutions, and the existence of nontrivial solutions under various assumptions and conditions, see for instance [3,7,12,13,17,19].…”