Existence and multiplicity results for the fractional Schrodinger-Poisson systems

Abstract

This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schrödinger-Poisson systems involving fractional Laplacian operator: \begin{equation}\label{eq*} \left\{ \aligned &(-Δ)^{s} u+V(x)u+ ϕu=f(x,u), \quad &\text{in }\mathbb{R}^3, &(-Δ)^{t} ϕ=u^2, \quad &\text{in }\mathbb{R}^3, \endaligned \right. \end{equation} where $(-\Delta {)}^{\alpha }$ stands for the fractional Laplacian of order $\alpha \in (0,1)$. Under certain assumptions on $V$ and $f$, we obtain infinitely many high energy solutions for \eqref{eq*} without assuming the Ambrosetti-Rabinowitz condition by using the fountain theorem.

References in corpus (4)

• Ground state solutions to the nonlinear Schrodinger-Maxwell equations
• Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
• On fractional Schrödinger equations in (\mathbb{R}^N) without the Ambrosetti-Rabinowitz condition
• Fractional Schrödinger-Poisson-Slater system in one dimension

Cited by in corpus (1)

• Fractional Schrodinger-Poisson Equations With General Nonlinearities