Existence Of Solutions Of Schr(o|")dinger-Poisson Systems With The Negative Non-local Term

Let us consider one kind of Schrodinger-Poisson equations with negative non-local term: We assume λ∈E (0,+∞) and 2< p< 6. In the critical growth conditions, by the Mountain Pass Theorem and variational methods, we can obtain the following result:Theorem 2.1. Suppose that λ∈E (0,+∞) and 2< p< 6 hold. Then the equation(SP) has a positive solution.Then we consider the other kind of Schrodinger-Poisson equations with negative non-local term: where the parameterλ∈E (0,+∞) and assume that the following conditions: (p)p∈(1,5);(a) a:R3â†'R+, and there exists a constant c> 0, such that a(x)> c for all x∈R3 and a(x)-c∈L(6/(5-p))(R3); (k) K:R3â†'R+and K ∈L2(R3).By the Mountain Pass Theorem and variational methods, we can get the fol-lowing result.Theorem 3.1. Suppose that (p), (a) and (k) hold. Then problem (P) has a positive ground state solution.