一类非线性薛定谔泊松方程的规范基态解

Normalized Ground State Solutions for a Class of Nonlinear Schrödinger-poisson Equation

本文研究了一类带有参数的非线性薛定谔泊松方程规范基态解的存在性.当参数μ<0时,通过分析Pohozaev流形的结构和泛函纤维映射的几何性质,应用极小化序列方法和Schwarz径向重排技术得到方程有一个正的规范基态解.当参数μ>0时,通过构造辅助泛函并应用形变引理得到了Pohozaev流形附近的一个(PS)序列,然后应用集中紧性原理和单调性方法得到方程规范基态解的存在性.

In this paper,we study the existence of normalized ground state solutions for a class of nonlinear Schrödinger-Poisson equation with parameters.When parameterμ<0,by analyzing the structure of Pohozaev manifold and the geometric properties of functional fiber mapping,the method of minimizing sequence and Schwarz radial rearrangement technique are applied to obtain a positive normalized ground state solution of the equation.When the parameterμ>0,a(PS)sequence near the Pohozaev manifold is obtained by constructing the auxiliary functional and applying the deformation lemma.Then,the existence of the normalized ground state solution of the equation is obtained by applying the concentration-compactness principle and the monotone method.