Boundness and Linearisation of a Class of Differential Equations with Piecewise Constant Argument

Abstract

The differential equations with piecewise constant argument (DE-PCAs, 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 result 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.

Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument

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Unpredictable solutions of quasilinear differential equations with generalized piecewise constant arguments of mixed type

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