无限滞后测度泛函微分方程的Ф-变差稳定性  

Ф-variational Stability for Measure Functional Differential Equations with Infinite Delay

作　　者：马学敏 张怀德 李宝麟[2] MA Xue-min;ZHANG Huai-de;LI Bao-lin(Teaching Department of Science,Gansu University of Chinese Medicine,Dingxi 743000;College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070)

机构地区：[1]甘肃中医药大学理科教学部,定西743000 [2]西北师范大学数学与信息科学学院,兰州730070

出　　处：《工程数学学报》2021年第1期121-135,共15页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10771171);甘肃省555创新人才工程(GS-555-CXRC);西北师范大学科技创新基金(NWNU-KJCXGC-212).

摘　　要：利用Φ-有界变差函数,本文讨论了无限滞后测度泛函微分方程的Φ-有界变差解的稳定性.给出了这类方程的Φ-变差稳定、Φ-变差吸引以及渐进Φ-变差稳定的定义,建立了其Φ-有界变差解的Φ-变差稳定性和渐进Φ-变差稳定性的Lyapunov型定理.所得结果是对无限滞后测度泛函微分方程的变差稳定性定理的本质推广.In the paper,by using the boundedΦ-variation function,the stability of the boundedΦ-variation solution to measure functional differential equations with infinite delay is discussed.With respect to this kind of equations,theΦ-variational stability,theΦ-variational attraction and asymptoticallyΦ-variational stability are defined.The Lyapunov type theorems for theΦ-variational stability and asymptoticallyΦ-variational stability of the boundedΦ-variation solutions are established.These results are essential generalization of the current variational stability theorem for measure functional differential equations with infinite delay.

关 键 词：无限滞后测度泛函微分方程 Φ-有界变差解 Φ-变差稳定性 渐近Φ-变差稳定性 LYAPUNOV函数 

分 类 号：O175.14[理学—基础数学]