Existence and multiplicity results for the fractional Schrodinger-Poisson systems

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 $(-Δ)^α$ stands for the fractional Laplacian of order $α\in (0\,,\,1)$. 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.

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