一类二阶时滞方程脉冲解的存在性与指数稳定性

基金项目:

国家自然科学基金数学天元基金;广东省自然科学基金

详细信息

Existence and impulsive stability for second order delaydifferential equation

摘要: 研究了一类二阶时滞微分方程,利用~Schaefer 不动点定理做工具论证了方程在脉冲条件下解的存在性, 通过构造合适的李雅普诺夫函数证明方程的非平凡解在区间 $[t_0,+\infty)$ 上是可脉冲指数稳定的,最后给出解可指数稳定的两个实例.
- Liapunov函数
Abstract: A class of the second order delayed differential equation is studied. Using Schaefer fixed point theorem, the existence of solution to the given model with impulse is proved and the proper Lyapunov functional is conducted to obtain that the nontrivial solution of the equation can be exponentially stabilized on $[t_0,+\infty)$ . Two examples are given in the end.
- Liapunov functional