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Normalized ground states for general pseudo-relativistic Schrödinger equations
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-11-19 , DOI: 10.1080/00036811.2020.1849631
Haijun Luo 1 , Dan Wu 1
Affiliation  

ABSTRACT

In this paper, we consider the pseudo-relativistic type Schrödinger equations with general nonlinearities. By studying the related constrained minimization problems, we obtain the existence of ground states via applying the concentration-compactness principle. Then some properties of the ground states have been discussed, including regularity, symmetry and etc. Furthermore, we prove that the set of minimizers is a stable set for the initial value problem of the equations, that is, a solution whose initial data is near the set will remain near it for all time.



中文翻译:

一般伪相对论薛定谔方程的归一化基态

摘要

在本文中,我们考虑具有一般非线性的伪相对论型薛定谔方程。通过研究相关的约束最小化问题,我们通过应用浓度-紧致性原理得到基态的存在性。然后讨论了基态的一些性质,包括规律性、对称性等。进一步证明了极小值集是方程初值问题的稳定集,即初始数据接近的解该装置将始终保持在它附近。

更新日期:2020-11-19
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