Multiplicity Of Solutions For Two Kinds Of Schr(?)dinger-Poisson Systems

In this paper,we first study the following autonomous Schr(?)dinger-Poisson system where f?C(R,R),and there exists ?>3 such that 1/?f(t)t? F(t)>,0 F(t)=?0t f(s)ds,t?R.We obtain infinitely many high energy radial solutions for the system by using a method generating a Palais-Smale sequence with an extra property related to Poho(?)aev identity and the minimax principle.Secondly,we consider system(0.0.1)with f(u)=a(x)|u|p-2u+?k(x)u,namely where p ?(2,3),?>0 small enough and ?>0.k(x)is a positive function,a(x)? C(R3)and a is sign changing,this is why we call it indefinite nonlineari-ty.We establish the multiple solutions of system(0.0.2)by using the symmetric mountain-pass theorem and a version of Clark's theorem.