Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682210Special Issue ( Nonlinear Analysis in Engineering and Sciences)20191201On a class of nonlinear fractional Schrödinger-Poisson systems123132440510.22075/ijnaa.2019.4405ENM.SolukiaDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranS.H.RasouliDepartment of Mathematics, Faculty of Basic Sciences, Babol (Noushirvani) University of Technology Babol, IranG.A.AfrouziDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranJournal Article20200516In this paper, we are concerned with the following fractional Schrödinger-Poisson system: (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, 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.https://ijnaa.semnan.ac.ir/article_4405_0d5ac99c730ccb355e764c67c563de52.pdf