【作者】 曹蕾；

【导师】 陈守信；

【作者基本信息】 河南大学 ， 应用数学， 2017， 硕士

【摘要】 本文主要研究在大流极限和Ambj(?)rn-Nielsen-Olesen (ANO)磁不稳定下一类阿贝尔涡旋和非阿贝尔涡旋的存在性.第一部分研究了阿贝尔涡旋中的特殊结构hole-vortex模型,其BPS方程可转化为一个二阶非线性常微分方程.利用射击法,我们建立了该问题解的存在唯一性定理,并在无穷远处给出了解的渐近性估计.第二部分研究了一类非阿贝尔涡旋模型,其BPS方程可转化为一个耦合的二阶常微分方程组,我们分别建立了方程组在紧区间[-R,R]和全直线R上解的存在性定理.在紧区间[-R,R]上,我们采用直接极小化方法建立了解的存在性,在全直线R上,我们引入带权空间并采用约束极小化方法建立了解的存在性.更多还原

【Abstract】 In this paper, we prove the existence for a class of Abelian vortex and non-Abelian vortex in the large flux limit and Ambj(?)rn-Nielsen-Olesen (ANO) magnetic instabilities.The first part is devoted to study a special structure of Abelian vortex which is called hole-vortex model. The BPS equations of the hole-vortex model can be changed to a second-order nonlinear ordinary differential equation. We establish the existence and uniqueness theorem for this problem by using a shooting method and present the gradual estimate at infinity under appropriate conditions. The second part is concentrated on the study of non-Abelian ordinary equations. We establish the existence theorems for the coupled second-order ordinary equations on the compact range [-R,R] and full line R.On the compact range [-R,R] we will use a direct minimization method to establish the existence of solutions. On the full line R , we will consider weighted space and use a constrained minimization method to establish the existence of solutions.更多还原