Ground State Sign-changing Solutions For The Nonlinear Fractional Schr(?)dinger-Poisson System

This paper is motivated by the study of the nonlinear fractional Schrodinger-Poisson systemwhere s,t?(0,1),2(s+t)>3 and V:R3?R is a potential function.Via a perturbation method combining the invariant sets of descending flow,we obtain a ground state sign-changing solution for the above system.In particular,for pure power type nonlinearity f(u)=|u|p-2u,we are concerned mostly with p?(4s+2t/s+t,4),a case in which few existence results are known compared with the case p ?(4,2s*).The outline of this paper is as follows:In section 1,we briefly introduce the background of these equations and main results.In section 2,for convenience,we present some notations of this thesis,then some preliminary results and variational framework of the above system are presented.In section 3,we introduce a perturbed problem and establish a compactness result.At last,section 4 is devoted to the proof of the main results.