The Existence,Multiplicity And Concentration Phenomenon Of Solutions For Fractional Schrodinger-poisson System

In this thesis,we first study the existence of solutions for the following fractional Schr?dinger-Poisson system where ? is a positive parameter,3/4<s<1 is a constant,h is a critical nonlinearty.Under some certain assumptions on h,we prove that the existence of positive ground state solution by variational methods.Furthermore,we consider the following fractional Schr?dinger-Poisson system with critical growth where ?>0 is a small parameter,3/4<s<1 is a constant,23*=6/3-2s is the fractional Sobolev critical exponent for 3-dimension,V:R3?R is a potential function,f is a sub-critical nonlinearty.Using variational methods and applying the Ljusternik-Schnirelmann category theorem,we prove that the existence of a positive ground state solution and the multiplicity of positive solutions.Finally,we study the existence and concentration of solutions for the following frac-tional Schr?dinger-Poisson system with competition potential where ?>0 s,2s*as above,4<p<2s*and V(x),K(x)?C(R3)??L?(R3)are positive potential function.Under some certain assumptions on V and K,we prove the existence of positive ground state solutions by Nehari manifold for e>0 sufficiently small.Moreover,we establish some properties of ground state solutions as ??0+,such as convergence,concentration and decay estimate.