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Existence and Properties of Solution of Nonlinear Differential Equations with Impulses at Variable Times
Version 1
: Received: 2 January 2024 / Approved: 3 January 2024 / Online: 3 January 2024 (10:04:47 CET)
A peer-reviewed article of this Preprint also exists.
Xia, H.; Peng, Y.; Zhang, P. Existence and Properties of the Solution of Nonlinear Differential Equations with Impulses at Variable Times. Axioms 2024, 13, 126. Xia, H.; Peng, Y.; Zhang, P. Existence and Properties of the Solution of Nonlinear Differential Equations with Impulses at Variable Times. Axioms 2024, 13, 126.
Abstract
In this paper, a class of nonlinear ordinary differential equations with impulses at variable times is considered. The existence and uniqueness of solution are given. At the same time, modifying the classical definitions of continuous dependence and Ga^teaux differentiability, some results on continuous dependence and Ga^teaux differentiable of solution relative to the initial value also are presented in new topology sense. For the autonomous impulsive system, the periodicity of solution is given. As an application, properties of solution for a type of controlled nonlinear ordinary differential equation with impulses at variable times is obtained. These results are foundation to study optimal control problems of systems governed by the differential equations with impulses at variable times.
Keywords
Differential equation; Impulses at variable times; Existence; Qualitative theory; Pulse phenomena
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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