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
DOI: 10.12677/AAM.2022.1111803, PDF,    国家自然科学基金支持
作者: 郭淑艳, 郭祖记*：太原理工大学数学学院，山西 晋中
关键词: 薛定谔泊松方程；变分法；规范解；基态解；Schr?dinger-Poisson Equations； Variational Methods； Normalized Solutions； Ground State Solutions
摘要: 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。
Abstract: In this paper, we study the existence of normalized solutions for a class of nonlinear Schrödinger- Poisson system. When parameter μ<0 , 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.
文章引用：郭淑艳, 郭祖记. 一类非线性薛定谔泊松方程规范解的存在性[J]. 应用数学进展, 2022, 11(11): 7583-7595. https://doi.org/10.12677/AAM.2022.1111803

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