一类非线性薛定谔泊松方程规范解的存在性

Existence of Normalized Solutions for a Class of Nonlinear Schr?dinger-Poisson Equations

本文研究了一类非线性薛定谔泊松方程规范解的存在性。在参数μ<0的情况下,首先分析了Pohozaev流形的结构和泛函纤维映射的几何性质,然后通过构造辅助泛函证明了能量泛函在Pohozaev流形附近存在一个有界的(PS)序列,最后应用集中紧性原理证明了方程正径向基态解和山路解的存在性。

In this paper, we study the existence of normalized solutions for a class of nonlinear Schr&#246;dinger- Poisson system. When parameter μ , firstly, the structure of Pohozaev manifold and the geo-metric properties of functional fiber mapping are analyzed, and then we prove the existence of a bounded (PS) sequence of energy functionals near the Pohozaev manifold by constructing auxiliary functional. Finally, the existence of the positive radial ground state solution and the mountain solu-tion of the equation is proved by the principle of concentration compactness.