一类二阶时滞微分方程脉冲解的存在性与指数稳定性

Existence and Exponential Stability of the Impulsive Solution for Delayed Differential Equations

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[t0,+∞)上是可脉冲指数稳定的,最后给出解可指数稳定的2个实例.

A class of the second order delayed differential equations 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 [ t0, ＋ ∞ ）. Two examples are given in the end.