فهرست نشریات علمی دسترسی آزاد ایران

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.