Schrdinger-Poisson方程的变号解的多解性（英文）

Multiple sign-changing solutions of the Schrdinger-Poisson equations

研究了非线性Schrdinger-Poisson系统{-Δu+u+λφ(x) u=|u|^(p-1)u, inR^3,-Δφ(x)=|u|~2, inR^3,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.

The existence of multiple sign-changing solutions for the following nonlinear Schr dinger-Poisson system：- Δ u＋u＋λφ（x）u= u p-1 u, in 0x0E？MT ExtraaBp0x0F 3,- Δ φ（x）= u 2, in 0x0E？MT ExtraaBp0x0F 3,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.