MMN-3785

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

Sebastián Lalvay; Adrián Padilla-Segarra; Walid Zouhair;

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;t] 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


Vol. 23 (2022), No. 1, pp. 295-310
DOI: 10.18514/MMN.2022.3785


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