一类具有强迫项的非线性方程的周期解

本文研究具有周期强迫项e(t)的非线性方程 (?) f(x)(?) g(x)=e(t) (1)的周期解。得到方程(1)存在周期解的充分条件的定理1和保证周期解的唯一性的定理解2和定理3.本文所得结果包含了[1]、[2]和[3]的第六章定理4.3,并且与[3]的第六章定理4.4和[4]的第六章定理8.2互不相包,但可避免[3]中要求f(x)∈C~1和估算解的界限的麻烦。显然,本文结果可用于锁相技术。

Periodic solution of a nonlinear equation with a forcing term

In this paper, We consider the periodic solution of the Lienard epuationWhere e(t) is a periodic function. We obtain Theorem 1 on sufficient conditions of the existence, and Theorem 2 and Theorem 3 on sufficient condition of the uniqueness for the peroidic solution of (1). The results of this paper extend the results in [1], [2] and Theorem 4. 3 of Chapter 6 in [3], and are different from Theorem 8. 2 of Chapter 6 in [4] and Theorem 4. 4 of Chapter 6 in [3].