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,
Universidad Yachay Tech, School of Mathematical and Computational Sciences, Hacienda San José S/N, 100115 Urcuquí, Imbabura, Ecuador,
sebastian.lalvay@yachaytech.edu.ec - Adrián Padilla-Segarra,
Universidad Yachay Tech, School of Mathematical and Computational Sciences, Hacienda San José S/N, 100115 Urcuquí, Imbabura, Ecuador,
adrian.padilla@yachaytech.edu.ec - Walid Zouhair,
Laboratory of Mathematics and Population Dynamics, Faculty of Sciences of Semlalia, Cadi Ayyad University, Marrakesh, BP 2390, 40000, Morocco,
walid.zouhair.fssm@gmail.com
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