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arXiv · 2601.01670

On existence, uniqueness and numerical approximation of impulsive differential equations with adaptive state-dependent delays using equations with piecewise-constant arguments

Ferenc Hartung
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Abstract

In this paper we consider a class of impulsive nonlinear differential equations with adaptive state-dependent delays. We discuss the existence and uniqueness of solutions of the initial value problem using a Picard-Lindel\"of type argument where we define approximate solutions with the help of equations with piecewise-constant arguments (EPCAs). Moreover, we show that the solutions of the associated EPCAs approximate the solutions of the original impulsive DDE with adaptive state-dependent delay uniformly on compact time intervals. The key assumption underlying both results is that the delayed time function is monotone, or piecewise strictly monotone.

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Ferenc Hartung. 2026-01-04. On existence, uniqueness and numerical approximation of impulsive differential equations with adaptive state-dependent delays using equations with piecewise-constant arguments. https://arxiv.org/abs/2601.01670

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