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

Miskolc Mathematical Notes

article

Sebastián Lalvay¹  Adrián Padilla-Segarra¹  Walid Zouhair² 

[1] Universidad Yachay Tech, School of Mathematical and Computational Sciences;Laboratory of Mathematics and Population Dynamics, Faculty of Sciences of Semlalia, Cadi Ayyad University

关键词: non-instantaneous impulses;    non-autonomous systems;    Karakostas’ fixed-point theorem;    evolution equations;    delay;    non-local conditions;   

DOI  :  10.18514/MMN.2022.3785

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

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, τ] 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.

【 授权许可】

CC BY