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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (1): 121-135.doi: 10.3969/j.issn.1005-3085.2021.01.011

• • 上一篇    下一篇

无限滞后测度泛函微分方程的$\Phi$-变差稳定性（英）

马学敏1,   张怀德1,   李宝麟2   

  1. 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
  • 收稿日期:2018-09-28 接受日期:2020-07-29 出版日期:2021-02-15 发布日期:2021-04-15
  • 基金资助:
    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).

$\Phi$-variational Stability for Measure Functional Differential Equations with Infinite Delay

MA Xue-min1,   ZHANG Huai-de1,   LI Bao-lin2   

  1. 1- Teaching Department of Science, Gansu University of Chinese Medicine, Dingxi 743000
    2- College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070
  • Received:2018-09-28 Accepted:2020-07-29 Online:2021-02-15 Published:2021-04-15
  • Supported by:
    The National Natural Science Foundation of China (10771171); the 555 Innovation Talent Project of Gansu Province (GS-555-CXRC); the Technique Innovation Project of Northwest Normal University (NWNU-KJCXGC-212).

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摘要： 利用$\Phi$-有界变差函数，本文讨论了无限滞后测度泛函微分方程的$\Phi$-有界变差解的稳定性．给出了这类方程的$\Phi$-变差稳定、$\Phi$-变差吸引以及渐进$\Phi$-变差稳定的定义，建立了其$\Phi$-有界变差解的$\Phi$-变差稳定性和渐进$\Phi$-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．

关键词: 无限滞后测度泛函微分方程, $\Phi$-有界变差解, $\Phi$-变差稳定性, 渐近$\Phi$-变差稳定性, Lyapunov函数

Abstract: In the paper, by using the bounded $\Phi$-variation function,the stability of the bounded $\Phi$-variation solution to measure functional differential equations with infinite delay is discussed. With respect to this kind of equations, the $\Phi$-variational stability, the $\Phi$-variational attraction and asymptotically $\Phi$-variational stability are defined. The Lyapunov type theorems for the $\Phi$-variational stability and asymptotically $\Phi$-variational stability of the bounded $\Phi$-variation solutions are established. These results are essential generalization of the current variational stability theorem for measure functional differential equations with infinite delay.

Key words: measure functional differential equations with infinite delay, bounded $\Phi$-variation solution, $\Phi$-variational stability, asymptotically $\Phi$-variational stability, Lyapunov function

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