Open AccessControllability of nonlinear ordinary differential equations with non-instantaneous impulses
Author(s) -
Zhen Xin,
AUTHOR_ID,
Yaning Yang,
Qiaoxia Li,
AUTHOR_ID
Publication year - 2022
Publication title -
mathematical modelling and control
Language(s) - English
Resource type - Journals
ISSN - 2767-8946
DOI - 10.3934/mmc.2022001
Subject(s) - controllability , mathematics , fixed point theorem , banach space , impulse (physics) , mathematical analysis , nonlinear system , ordinary differential equation , c0 semigroup , initial value problem , schauder fixed point theorem , pure mathematics , picard–lindelöf theorem , differential equation , physics , quantum mechanics
In this paper, we consider controllability of the initial value problem with non-instantaneous impulse on ordered Banach spaces. We firstly give a solution expression for initial value problems with non-instantaneous impulses in ordered Banach Spaces by using Schauder fixed point theorem. Sufficient conditions for controllability results are obtained by Krasnoselskii's fixed point theorem in the infinite-dimensional spaces. An example is also given to illustrate the feasibility of our theoretical results.