A Grobman-Hartman theorem for a differential equation with piecewise constant generalized argument

Manuel Pinto; Gonzalo Robledo

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arXiv · 1506.00533

A Grobman-Hartman theorem for a differential equation with piecewise constant generalized argument

Manuel Pinto·Gonzalo Robledo

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Abstract

We obtain sufficient conditions ensuring the existence of a uniformly continuous and H\"older continuous homeomorphism between the solutions of a linear system of differential equations with piecewise constant argument of generalized type and the solutions of the quasilinear corresponding system. We use a definition (recently introduced by M. Akhmet) of exponential dichotomy for those systems combined with technical assumptions on the nonlinear part. Our result generalizes a previous work of G. Papaschinopoulos.

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Manuel Pinto, Gonzalo Robledo. 2015-06-01. A Grobman-Hartman theorem for a differential equation with piecewise constant generalized argument. https://arxiv.org/abs/1506.00533

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