分离性与回复解和概周期解的存在性

本文主要是研究微分方程组的回复解和概周期解的问题。在§2中,我们研究了一般回复系统和自治系统,证明了回复系统存在有限个可分离的有界解这一性质是可继承的。还证明了自治系统的回复解与概周期解的存在及不存在性定理。在§3中,研究一般概周期系统,讨论了其概周期解和渐近概周期解与分离性之间的某些关系。

SEPARABILITY AND THE EXISTENCE OF RECURRENT SOLUTIONS AND ALMOST PERIODIC SOLUTIONS

The main object of this paper is to study the problems of recurrent and almost periodic solutions of differential equations. In section 2, the author proves that the property which recurrent system has k separable bounded solutions is inheritable, and gives the existence and non-existence theorems of recurrent (or almost periodic) solutions of autonomous and nonautonomous differential equations. In section 3, the author discusses some relationships among the separabilities and the almost periodic and asymptotically almost periodic solutions of almost periodic system.