Differentiability of Semi-Flow for Impulsive Evolution Equation with State-Dependent Delay

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-09-18 DOI:10.1007/s12346-024-01134-5

Weifeng Ma, Yongxiang Li

引用次数: 0

Abstract

In this paper, we study the impulsive evolution equation with state-dependent delay by the theory of operator semigroup in Banach spaces. Under conditions that both nonlinearity and impulsive functions are Lipschitz continuous, we obtain the existence and uniqueness results of mild solution. Furthermore, we prove the differentiability of a semi-flow defined by a continuously differentiable solution operator under the appropriate condition.

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带状态延迟的脉冲演化方程的半流可微分性

本文利用巴拿赫空间中的算子半群理论研究了具有状态相关延迟的脉冲演化方程。在非线性和脉冲函数均为 Lipschitz 连续的条件下，我们得到了温和解的存在性和唯一性结果。此外，我们还在适当条件下证明了连续可微解算子定义的半流的可微性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.