一类时滞Liénard方程同宿解存在性问题

Existence of homoclinic solutions for a class of Liénard equation with delay

本文首先利用Mawhin重合度拓展定理对任意正整数k探讨了一类时滞Liénard方程2kT-周期解uk(t)存在性问题,由此获得周期函数集合{uk(t)},然后证明了该集合{uk(t)}在Cl1oc(R,R)中的极限点就是所讨论方程的同宿解.

By means of Mawhin＇ s continuation theorem and some analysis methods, the existence of a set with 2kT -periodic solutions uk （t） for a class of Li6nard equation with a delay is studied for each positive integer k, and then a homoclinic solutions is obtained as any limit point of the set {uk （t） } in the space of Ckx, （R,R）.