普通型二分性与Favard定理

ORDINARY DICHOTOMIES AND FAVARD THEOREM

本文我们首先推广了著名的Ｆａｖａｒｄ定理并指出对齐次线性概周期系统由Ｆａｖａｒｄ定理所得到的概周期解是平凡的．然后利用推广后的Ｆａｖａｒｄ定理和普通型二分性讨论了一类线性和非线性系统的概周期解存在性．Ｎａｋａｊｉｍａ在文［３］中的结果是我们的结果的一种特殊情形．

In this paper we first extend Favard theorem and point out that for homogeneous linear almost periodic systems the almost periodic solutions followed from Favard theorem are trivial,then discuss the existence of almost periodic solutions of a type of linear and nonlinear systems by making use of extended Favard theorem and ordinary dichotomies.Nakajima's results in [3] are the special case of our results.