光涡旋方程解的存在性研究

Existence of Optical Vortex Solution

现代物理光学领域里,光涡旋的相变引起的奇性是当今研究的重点.本论文将讨论一类非线性薛定谔方程,涡旋解的存在性.我们得到两个结果,第一个是采用山路定理证明方程解的存在性.第二个结果是关于约束极小解的存在性,并讨论拉格朗日乘数的下界问题.

In this paper,we consider a typical model developed in the study of optical vortices. We prove two existence results of vortex solution of a class of nonlinear Schrodinger equation. The first one is obtained by mountain pass theorem,and the second one by constrained minimization approach.