带周期位势平面薛定谔-泊松方程组的结点解

Nodal solutions for a class of planar Schrdinger-Poisson systems with periodic potential

利用临界点理论中的亏格定理和Nehari流形技巧,本文证明了在二维全空间上一类带周期位势的薛定谔-泊松方程组高能量解的存在性,且该解存在无穷多个结点区域.更进一步,得到了其基态解的存在性且是不变号的.

In this paper,using genus theorem and Nehari manifold techniques in critical points theory, we prove the existence of high energy solutions for a class of SchrSdinger-Poisson systems with periodic potential in dimension two, and obtain that the solution has infinitely nodal domains. Furthermore, the existence of ground state solution is proved which does not change sign