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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.01670 |
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| _version_ | 1866914233185206272 |
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| author | Hartung, Ferenc |
| author_facet | Hartung, Ferenc |
| contents | 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-Lindelöf 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01670 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On existence, uniqueness and numerical approximation of impulsive differential equations with adaptive state-dependent delays using equations with piecewise-constant arguments Hartung, Ferenc Dynamical Systems 34K43, 34K45, 65L03 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-Lindelöf 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. |
| title | On existence, uniqueness and numerical approximation of impulsive differential equations with adaptive state-dependent delays using equations with piecewise-constant arguments |
| topic | Dynamical Systems 34K43, 34K45, 65L03 |
| url | https://arxiv.org/abs/2601.01670 |