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arXiv · 2203.05905

On the existence and uniqueness of solutions for non-autonomous semi-linear systems with non-instantaneous impulses, delay, and non-local conditions

Sebastiàn Lalvay·Adriàn Padilla-segarra·Walid Zouhair
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Abstract

A non-autonomous evolution semi-linear differential system under non-instantaneous impulses, delays, and perturbed by non-local conditions is studied. Its piece-wise continuous solutions belong to a finite-dimensional Banach space. The existence and uniqueness of solutions on the interval $[-r,\tau]$ are obtained by applying Karakostas fixed-point theorem. Further results concerning solution prolongation are developed. An example is presented, and several remarks on the infinite-dimensional case are included.

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Sebastiàn Lalvay, Adriàn Padilla-segarra, Walid Zouhair. 2022-03-11. On the existence and uniqueness of solutions for non-autonomous semi-linear systems with non-instantaneous impulses, delay, and non-local conditions. https://arxiv.org/abs/2203.05905

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