Document Type : Special issue editorial

Authors

• A. Keyhanfar ¹
• S.H. Rasouli ²
• G.A. Afrouzi ¹

¹ Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

² Department of Mathematics, Faculty of Basisc Sciences, Babol(Noshirvani) University of Technology Babol, Iran

Abstract

In this paper, we are concerned with the following fractional Schrödinger-Poisson system: 
$$\{\begin{array}{ll}(-{\mathrm{\Delta }}^s)u+u+\lambda \varphi u=\mu f(n)+|u{|}^{p-2}|u|,& x\in {\mathbb{R}}^3\\ (-{\mathrm{\Delta }}^t)\varphi =u^2,& x\in {\mathbb{R}}^3\end{array}$$
where $\lambda ,\mu$ are two parameters, $s,t\in (0,1],2t+4s>3,1<p\le 2_s^{\ast }$ and $f:\mathbb{R}⟶\mathbb{R}$ is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with the help of the vibrational methods.

Keywords

• Fractional Schrödinger-Poisson systems
• Sublinear nonlinearity
• Variational methods