Abstract

In this paper, we develop the theory of differential equations with mixed perturbations of the second type on time scales. We give an existence theorem for differential equations with mixed perturbations of the second type on time scales under Lipschitz condition. We also present some fundamental differential inequalities on time scales, which are utilized to investigate the existence of extremal solutions. We establish the comparison principle for differential equations with mixed perturbations of the second type on time scales. Our results in this paper extend and improve some well-known results.

Details

Title
Basic theory of differential equations with mixed perturbations of the second type on time scales
Author
Zhao, Yige 1   VIAFID ORCID Logo  ; Sun, Yibing 1 ; Liu, Zhi 2 ; Bai, Zhanbing 3 

1  School of Mathematical Sciences, University of Jinan, Jinan, P.R. China 
2  School of Automation and Electrical Engineering, Key Laboratory of Complex systems and Intelligent Computing in Universities of Shandong, Linyi University, Linyi, P.R. China 
3  College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, P.R. China 
Pages
1-15
Publication year
2019
Publication date
Jul 2019
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13662-019-2212-3
ProQuest document ID
2251955591
Copyright
Advances in Difference Equations is a copyright of Springer, (2019). All Rights Reserved., © 2019. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.