DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM

Abstract

In this paper, we study the following nonlinear fractional Schrödinger-Poisson system

$\begin{equation*}\left\{\begin{array}{ll}(-\Delta)^{s}u+\lambda V(x)u+\mu\phi u=|u|^{p-2}u, & \hbox{in}\; \mathbb{R}^3 , \\(-\Delta)^{s}\phi=u^{2}, & \hbox{in}\; \mathbb{R}^3, \end{array}\right.\end{equation*}$ where \begin{document}$s\in(\frac{3}{4}, 1)$\end{document}, \begin{document}$ 2, \begin{document}$\lambda, \mu$\end{document} are positive parameters and the potential \begin{document}$V(x)$\end{document} is a nonnegative continuous function with a potential well \begin{document}$\Omega=int V^{-1}(0)$\end{document}. By establishing truncation technique and the parameter-dependent compactness lemma, the existence, decay rate and asymptotic behavior of positive solutions are established. Moreover, we prove some nonexistence results in the case of \begin{document}$ 2.