The existence and multiplicity of solutions of a fractional Schrdinger-Poisson system with critical growth

In this paper, we study the existence and multiplicity of solutions for the following fractional Schrodinger-Poisson system：（{ε2S（-△）Su＋V（x）u＋φu=｜u｜2＊s-2＋f（u）in R3ε2s（-△）sφ=u in R3（0.1）where 3/4〈s〈1,2＊：＋6/3-2s）is the fractional critical exponent for 3-dimension, the potential V ： R3→ R is continuous and has global minima, and f is continuous and supercubic but subcritical at infinity. We prove the existence and multiplicity of solutions for System （0.1） via variational methods.

In this paper, we study the existence and multiplicity of solutions for the following fractional Schr¨odinger-Poisson system:ε^(2s)(-?)~su + V(x)u + ?u = |u|~2_s~*-2 u + f(u) in R^3,ε^(2s)(-?)~s? = u^2 in R^3,(0.1)where 3/4< s < 1, 2_s~*:=6/(3-2s)is the fractional critical exponent for 3-dimension, the potential V : R^3→ R is continuous and has global minima, and f is continuous and supercubic but subcritical at infinity. We prove the existence and multiplicity of solutions for System(0.1) via variational methods.