Open AccessStability analysis for $ (\omega, c) $-periodic non-instantaneous impulsive differential equations
Author(s) -
Kui Liu
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022101
Subject(s) - exponential stability , mathematics , omega , mathematical analysis , exponential function , nonlinear system , differential equation , stability (learning theory) , cauchy distribution , correctness , physics , computer science , algorithm , quantum mechanics , machine learning
In this paper, the stability of $ (\omega, c) $-periodic solutions of non-instantaneous impulses differential equations is studied. The exponential stability of homogeneous linear non-instantaneous impulsive problems is studied by using Cauchy matrix, and some sufficient conditions for exponential stability are obtained. Further, by using Gronwall inequality, sufficient conditions for exponential stability of $ (\omega, c) $-periodic solutions of nonlinear noninstantaneous impulsive problems are established. Finally, some examples are given to illustrate the correctness of the conclusion.