一类薛定谔-泊松方程解的存在性

Existence Results for a Schrdinger-Poisson Equation

本文研究一类具有变号权的薛定谔-泊松方程-Δu+u+k(x)φu=a(x)|u|p-1u,x∈R3,-Δφ=k(x)u2,x∈R3解的存在性,其中3≤p<5,a(x)为一连续的变号权且lim|x|→∞=a∞<0,k(x)连续且k(x)∈L2(R3).我们将证明该方程至少存在一个非平凡的解.

In this paper,we are concerned with the existence result of{-Δu＋u＋k（x）φu=a（x）｜u｜p-1u,x∈R3,-Δφ=k（x）u2,x∈R3,where 3≤p5,a（x） is a continuous and sign-changing function in R3 with lim｜x｜→∞=a∞0,k（x） is continuous and k（x）∈L2（R3）.We will prove that the problem has at least one nontrivial solution.