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

作　　者：胡猛[1] 吕海燕[1] HU Meng;LV Haiyan(School of Mathematics and Statistics,Anyang Normal University,Anyang 455000,China)

机构地区：[1]安阳师范学院数学与统计学院,河南安阳455000

出　　处：《应用数学》2021年第1期194-203,共10页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11801012);the Key Scientific Research Project of Colleges and Universities of Henan Province (21A110001)。

摘　　要：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.

关 键 词：时标 积分-微分方程 SCHAUDER不动点定理 δ±移位周期解 正解 指数稳定 

分 类 号：O175.6[理学—数学]