一类具有逐段常数变元的微分方程的有界性与线性化
Boundness and Linearisation of a class of differential equations with piecewise constant argument
摘要：
具有分段常数变元的微分方程（DEPCA）是一类混合动力系统（结合了连续和离散）。本文在非线性项部分无界的假设下，研究了一类一般型DEPCA的有界解和全局拓扑线性化。本文的目的之一是得到一个新的判别准则，该准则改进了以前的结果。本文的另一个目的是建立非线性扰动系统与其线性系拓扑共轭的广义Grobman-Hartman型定理。该方法是基于新获得的有界解的标准。所得结果推广和改进了以往的一些文献。采用了一些新的技术。
英文摘要：
The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded, we study the bounded solution and global topological linearisation of a class of DEPCAs of general type. One of the purpose of this paper is to obtain a new criterion for the existence of a unique bounded solution, which improved the previous results. The other aim of this paper is to establish a generalized Grobman-Hartman-type theorem for the topological conjugacy between a nonlinear perturbation system and its linear system. The method is based on the new obtained criterion for bounded solution. The obtained results generalized and improved some previous papers. Some novel techniques are employed.
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