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Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses

  • Dan Yang and JinRong Wang EMAIL logo
Published/Copyright: February 25, 2025
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Abstract

In this paper, we investigate the orbital Hausdorff continuous dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses. The concepts of orbital Hausdorff continuous dependence and stability are used to characterize the relations of solution corresponding to the impulsive moments and the difference between the impulsive moments and the junction points in the sense of the Hausdorff distance. Then, we establish sufficient conditions to guarantee the orbital Hausdorff continuous dependence and stability on their respective trajectories. Finally, two examples are given to illustrate our theoretical results.

MSC 2010: 34A08; 34A12; 34D20; 34A37

This work was partially supported by the National Natural Science Foundation of China, Grant No. 12161015 and Gui’an Kechuang Company & Guizhou University Joint Data Shield Laboratory Project (No. GAKC070801-2024).


  1. (Communicated by Michal Fečkan)

Acknowledgement

The authors want to thank the reviewers for spending their precious time to read this manuscript and insightful comments that helped improve the presentation of this article.

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Received: 2024-05-25
Accepted: 2024-09-09
Published Online: 2025-02-25
Published in Print: 2025-02-25

© 2025 Mathematical Institute Slovak Academy of Sciences

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