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Existence on solutions of a class of casual differential equations on a time scale

  • Yige Zhao EMAIL logo
Published/Copyright: June 8, 2021
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Abstract

In this paper, we develop the theory of a class of casual differential equations on a time scale. An existence theorem for casual differential equations on a time scale is given under mixed Lipschitz and compactness conditions by the fixed point theorem in Banach algebra due to Dhage. Some fundamental differential inequalities on a time scale are also presented which are utilized to investigate the existence of extremal solutions. The comparison principle on casual differential equations on a time scale is established. Our results in this paper extend and improve some well-known results.

MSC 2010: Primary 34N05; 34A12

This work was supported by the National Natural Science Foundation of China (61703180, 61803176, 61877028, 61807015, 61773010), the Natural Science Foundation of Shandong Province (ZR2019MF032, ZR2017BA010), the Project of Shandong Province Higher Educational Science and Technology Program (J18KA230, J17KA157), and the Scientific Research Foundation of University of Jinan (1008399, 160100101).


  1. (Communicated by Michal Fečkan)

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Received: 2019-10-10
Accepted: 2020-07-28
Published Online: 2021-06-08
Published in Print: 2021-06-25

© 2021 Mathematical Institute Slovak Academy of Sciences

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