一类三阶中立型泛函微分方程同宿轨的存在性

Existence of homoclinic orbits for a class of three order neutral functional differential equations

利用Mawhin重合度理论,研究了一类三阶中立型泛函微分方程同宿轨的存在性.运用一些分析技巧对先验界做出估计,对一列周期解取极限,得到了所研究的方程具有一个非平凡的同宿轨.

The existence of homoclinic orbits for a class of third-order neutral functional differential equations was studied by using Mawhin coincidence degree theory. By using some analytical techniques to estimate the priori bounds and to extract the limit of a series of periodic solutions,it was obtained that the equation studied had a nontrivial homoclinic orbit.