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A Delay Differential Equation with an Impulsive Self-Support Condition

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Abstract

The object of study is an autonomous impulsive system proposed as a model of drugs absorption by living organisms consisting of a linear differential delay equation and an impulsive self-support condition. We get a representation of the general solution in terms of the fundamental solution of the differential delay equation. The impulsive self-support generates periodic auto-oscillations given by fixed points of a first return map.

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Correspondence to J. G. Mesquita.

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M. Federson: Supported by FAPESP Grant 2017/13795-2 and CNPq Grant 309344/2017-4. J.G. Mesquita: Supported by FAPESP Grant 2013/17104-3 and 2014/04732-9.

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Federson, M., Györi, I., Mesquita, J.G. et al. A Delay Differential Equation with an Impulsive Self-Support Condition. J Dyn Diff Equat 32, 605–614 (2020). https://doi.org/10.1007/s10884-019-09750-5

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  • DOI: https://doi.org/10.1007/s10884-019-09750-5

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