一类Kirchhoff-Schr dinger-Poisson方程的非平凡解

Nontrivial Solutions to a Class of Kirchhoff-Schr dinger-Poisson Equation

-a+b∫R 3 u 2 d xΔu+u+λ∅u=a(x)u p-2 u,u∈H(R 3)-Δ∅=u 2,∅∈D 1,2(R 3)为一类非自治的Kirchhoff-Schr dinger-Poisson方程,其中,a>0,λ>0,b≥0,4<p<6,a(x)∈C(R 3)且a(x)为变号。对a(x)赋予适当的条件,通过变分法、山路定理和一些分析技巧,给出了该方程的非平凡解的存在性定理,并利用强极值原理得到了它的正解。

-(a+b∫R 3|u|2 d x)Δu+u+λ∅u=a(x)|u|p-2 u,u∈H(R 3)-Δ∅=u 2,∅∈D 1,2(R 3)was the nonautonomous Kirchhoff-Schr dinger-Poisson equation,where a>0,λ>0,b≥0,4<p<6,a(x)∈C(R 3)and a(x)is sign changing.The existence theorem for nontrivial solution was obtained by variational method,mountain pass theorem and some analytical techniques under appropriate conditions for a(x).The positive solution of the problem was obtained by using strong maximum principle.