Abstract

We introduce the concepts of Poisson boundedness and partial Poisson boundedness for a solution of a differential system. These properties mean that the solution or, respectively, its projection onto a given subspace is contained in some ball for the values of an independent variable belonging to countably many intervals converging to infinity. Based on the method of Lyapunov vector functions and the Krasnosel’skii canonical domain method, sufficient conditions are obtained for the existence of such solutions.

中文翻译：

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Lyapunov向量函数，Krasnosel'skii正则域和Poisson有界解的存在

摘要

我们介绍了泊松有界和局部泊松有界的概念，用于求解微分系统。这些特性意味着，对于一个自变量的值，该解决方案或其在给定子空间上的投影分别包含在某个球中，该自变量的值属于无数个收敛到无穷大的区间。基于Lyapunov向量函数的方法和Krasnosel'skii规范域方法，为此类解的存在获得了充分的条件。