二阶线性脉冲时滞微分方程的基本解

郭青宏; 赵爱民

您当前的位置：

首页 >

文章列表页 >

二阶线性脉冲时滞微分方程的基本解

更新时间：2026-09-14

- 二阶线性脉冲时滞微分方程的基本解
- 二阶线性脉冲时滞微分方程的基本解
- Issue 2, (2006)
- 作者机构：
  
  山西大学数学科学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2006
- 稿件说明：
移动端阅览
郭青宏, 赵爱民. 二阶线性脉冲时滞微分方程的基本解[J]. 2006, (2).
DOI：

郭青宏, 赵爱民. 二阶线性脉冲时滞微分方程的基本解[J]. 2006, (2). DOI：

摘要

考虑带有阻尼项的二阶线性脉冲时滞微分方程.利用脉冲微分不等式和脉冲积分不等式理论

证明了对应于方程的基本解X(t

s)及其导数Xt′(t

s)在任一平面区域[t0

b)×[t0

b)内是有界的.应用L ebesgue控制收敛定理证明了具有齐次脉冲条件且初始函数满足φ(t)=0时初始问题的解可由函数X(t

s)f(s)的积分表示.最后给出了一般初始问题解的积分表示.B erezansky and B raverm an的结论是本文结果中阻尼项系数a(t)=0的特殊情形.

Abstract

This paper aims to acquire the fundamental solutions to second-order linear impulsive time-lag differential equations with damping term(SLIDE).By using the theory on impulsive differential inequalities and impulsive integral inequalities

the authors have proved that the fundamental solution X(t

s) to SLIDE and its derivative X~′

s) are bounded on [t

b)×[t

b).By using Lebesgue dominant convergence theorem

the authors have proved that the solutions to initial value problem with homogeneous impulsive effect and initial function φ(t)=0 can be represented by \$x(t)=∫

_t_0X(t

s)f(s)ds\$

where f(t) being the forcing term of the equation.The findings by Berezansky and Braverman are merely the special cases when the coefficient of damping term a(t)=0.

关键词

Keywords

references

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Research Progress on Single⁃Photon Detection for Quantum Information About Mechanisms，Devices and Circuit Design

Adaptive Shock Wave Overpressure Sensing for Dynamic Explosion Testing

Study on the Ultrasonic Adsorption of Cr（Ⅵ） in Water by Tea Biochar Magnetic Materials

机器人机构设计与控制专栏

PEG⁃Like Polymers Based on Low Molecular Weight PEI as Gene Vectors

Related Author

No data

Related Institution

No data

⁰