EXISTENCE OF THE NORMALIZED SOLUTIONS TO THE NONLOCAL ELLIPTIC SYSTEM WITH PARTIAL CONFINEMENT
EXISTENCE OF THE NORMALIZED SOLUTIONS TO THE NONLOCAL ELLIPTIC SYSTEM WITH PARTIAL CONFINEMENT
复制标题
具有部分约束的非局部椭圆系统归一化解的存在性
DOI：
10.3934/dcds.2019092
复制
发表时间：
2019
影响因子：
1.1
通讯作者：
Zhu Maochun
中科院分区：
文献类型：
--
作者：
Wang Jun;Geng Qiuping;Zhu Maochun
本文研究了部分约束的非局域椭圆系统驻波的存在性及其轨道稳定性。这种类型的方程源自少量电子与静态原子核相互作用的基本量子化学模型。一方面，我们证明了受 \begin{document}$ L^2 $\end{document} 约束的关联能量函数的全局最小化的存在性。另一方面，我们讨论全局极小值的轨道稳定性。与本地情况相比，我们需要建立与斯坦纳重排相关的新的不等式。
In present paper we study the existence and orbital stability of the standing waves to the nonlocal elliptic system with partial confinement. This type equations arises from the basic quantum chemistry model of small number of electrons interacting with static nucleii. On the one hand, we prove the existence of global minimizer of the associate energy functional subject to the \begin{document}$ L^2 $\end{document} -constraint. On the other hand, we discuss the orbital stability of the global minimizers. Comparing to the local case, we need establish the new inequality related to the Steiner rearrangement.