脉冲无穷时滞中立型测度微分方程mild解的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1671-1681.

脉冲无穷时滞中立型测度微分方程mild解的存在性

刘文杰^1,*(),谢胜利²()

¹ 安徽城市管理职业学院公共教学部, 合肥 230011
² 安徽建筑大学数理学院, 合肥 230601

收稿日期:2021-11-12 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 刘文杰 E-mail:2020035@cua.edu.cn;slxie@ahjzu.edu.cn
作者简介:谢胜利, E-mail: slxie@ahjzu.edu.cn
基金资助:
安徽省自然科学基金(1508085MA08);安徽省教育厅自然科学基金(KJ2014A043);安徽城市管理职业学院重点科研项目(2021zrkx03)

Existence Results of Mild Solutions for Impulsive Neutral Measure Differential Equations with Infinite Delay

Wenjie Liu^1,*(),Shengli Xie²()

¹ Public Curriculum Department, Anhui Vocational College of City Management, Hefei 230011
² School of Mathematics & Physics, Anhui University of Architecture, Hefei 230601

Received:2021-11-12 Online:2022-12-26 Published:2022-12-16
Contact: Wenjie Liu E-mail:2020035@cua.edu.cn;slxie@ahjzu.edu.cn
Supported by:
NSF of Anhui Province(1508085MA08);the NSF of Anhui Provincial Education Department(KJ2014A043);the Key Project of Anhui Vocational College of City Management(2021zrkx03)

摘要/Abstract

摘要：

该文主要研究无穷时滞脉冲中立型测度微分方程mild解的存在性.在半群非紧的条件下, 通过运用算子半群理论、Kuratowski非紧性测度、Mönch不动点定理及分段估计的方法得出方程mild解存在的充分条件.没有使用先验估计和非紧性限制条件, 推广许多已有的结果.最后, 给出一个实例说明结果的可行性.

关键词: 脉冲中立型测度微分方程, Mild解, Kuratowski非紧性测度, 不动点定理

Abstract:

In this paper, we mainly examine the existence of mild solutions for impulsive neutral measure differential equations with infinite delay. Under the condition that semigroups are non-compact, we obtain sufficient conditions for the existence of mild solutions by using operator semigroup theory, Kuratowski measure of noncompactness, Mönch fixed point theorem and piecewise estimation. Without utilizing a priori estimation and non-compact constraints, we generalize many existing results. Finally, an example is delivered to illustrate the feasibility of the result.

Key words: Impulsive neutral measure differential equations with infinite delay, Mild solution, Kuratowski measure of noncompactness, Fixed point theorem

中图分类号:

O175.15

刘文杰,谢胜利. 脉冲无穷时滞中立型测度微分方程mild解的存在性[J]. 数学物理学报, 2022, 42(6): 1671-1681.

Wenjie Liu,Shengli Xie. Existence Results of Mild Solutions for Impulsive Neutral Measure Differential Equations with Infinite Delay[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1671-1681.

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