On a class of nonlinear fractional Schrödinger-Poisson systems

Soluki, M.; Rasouli, S.H.; Afrouzi, G.A.

doi:10.22075/ijnaa.2019.4405

On a class of nonlinear fractional Schrödinger-Poisson systems

Document Type : Special issue editorial

Authors

M. Soluki 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 Basic Sciences, Babol (Noushirvani) University of Technology Babol, Iran

10.22075/ijnaa.2019.4405

Abstract

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:
$$\left\{
\begin{array}{ll}
(-\Delta^s)u+V(x)u+\phi u=m(x)|u|^{q-2}|u|+f(x,u), & x\in\Omega, \\
(-\Delta^t)\phi=u^2, & x\in\Omega,\\
u=\phi=0, & x\in\partial\Omega
\end{array}
\right.$$

where $s,t \in (0,1], 2t + 4s > 3, 1 < q < 2$ and $\Omega$ is a bounded smooth domain of $\mathbb{R}^3$, and $f(x,u)$ is linearly bounded in $u$ at infinity. Under some assumptions on $m, V$ and $f$ we obtain the existence of non-trivial solutions with the help of the variational methods.

Keywords

Fractional Schrödinger-Poisson systems

Non-trivial solutions

Variational methods