时标上具时滞积分-微分方程正解的存在性与稳定性

Existence and Stability of Positive Solutions to Nonlinear Delay Integro-Differential Equation on Time Scales

本文研究时标上一类具时滞积分-微分方程的正解的存在性与稳定性.运用Schauder不动点定理和时标上动力学方程分析理论,分别得到方程存在正δ±移位周期解和正解的充分条件,及正解指数稳定的充分条件.最后,通过两个数值例子来说明结果的可行性.

This paper studies the existence and stability of positive solutions for a class of nonlinear delay integro-differential equation on time scales.By using Schauder’s fixed point theorem and the theory of dynamic equations on time scales,sufficient conditions for the existence of positive periodic solutions in shifts δ_± and positive solutions,and sufficient conditions for the exponential stability of positive solution of the equation are obtained,respectively.Finally,two examples are given to illustrate the usefulness of the main results.