摘要 研究了非线性Schrodinger-Poisson系统－Δu+u+λφ(x)u=|u|p-1u,in R3,－Δφ=|u|2, in R3，的多变号解的存在性．利用下降流线的不变集方法，证明了该系统对ｐ∈（３，５）具有无穷多变号解并存在一个最小势能的变号解．文献中很少见到该系统多变号解的存在结果，推广了文献中的一些结论．
Abstract：The existence of multiple sign-changing solutions for the following nonlinear Schrodinger-Poisson system:－Δu+u+λφ(x)u=|u|p-1u,in R3,－Δφ=|u|2, in R3, was studied.By using a method of invariant sets of descending flow, it was proved that this system had infinitely many sign-changing solutions and had a least energy radially sign-changing solution for p∈(3, 5) .Few existence results of multiple sign-changing solutions were available in the literature.Some results in literature were improved.
2018, Vol. 31 
