一维向列相液晶模型方程孤立波解的存在性

Existence of Solitary Wave Solutions for One-dimensional Nematic Liquid Crystals Model Equations

在证明W^(1,2)(-∞,+∞)空间中向列相液晶模型方程孤立波解的存在性的过程中,关键是要证明相关的泛函是紧性的.因此,首先可根据临界点理论中的集中紧性原理的方法,证明二分性以及消失性不成立,即在W^(1,2)(-∞,+∞)空间中泛函的极小化序列的紧性是成立的,进一步利用极值原理的方法,得到一维向列相液晶模型方程孤立波解的存在性.

In the process of proving the existence of solitary wave solutions for one-dimensional nematic liquid crystal model equations in W^（1,2）（- ∞,＋ ∞）,the key point is to prove that the relevant functional is compact.Therefore,firstly,using the method of concentrated-compactness principle in the critical points theory,two bad cases：dichotomy and vanishing were eliminated,and prove the compactness of the minimizing sequences was proved.Then,the existence of solitary wave solutions for one-dimensional nematic liquid crystal model equations was obtained by using the extremum principle.