Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems
In this paper, we study the existence and uniqueness of second-order impulsive delay differential systems. Firstly, we define cosine-type and sine-type delay matrix functions, which are used to derive the solutions of the impulsive delay differential systems. Secondly, based on the Schauder and Bana...
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2024-11-01
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| author | Yingxia Zhou Mengmeng Li |
| author_facet | Yingxia Zhou Mengmeng Li |
| author_sort | Yingxia Zhou |
| collection | DOAJ |
| description | In this paper, we study the existence and uniqueness of second-order impulsive delay differential systems. Firstly, we define cosine-type and sine-type delay matrix functions, which are used to derive the solutions of the impulsive delay differential systems. Secondly, based on the Schauder and Banach fixed-point theorems, we establish sufficient conditions that guarantee the existence and uniqueness of solutions to nonlinear impulsive delay differential systems. Finally, several examples are given to illustrate our theoretical results. |
| format | Article |
| id | doaj-art-3631de6fff174e3fa8ac5e69b2e7f25e |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-3631de6fff174e3fa8ac5e69b2e7f25e2025-08-20T02:00:51ZengMDPI AGAxioms2075-16802024-11-01131283410.3390/axioms13120834Existence and Uniqueness of Second-Order Impulsive Delay Differential SystemsYingxia Zhou0Mengmeng Li1Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaDepartment of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaIn this paper, we study the existence and uniqueness of second-order impulsive delay differential systems. Firstly, we define cosine-type and sine-type delay matrix functions, which are used to derive the solutions of the impulsive delay differential systems. Secondly, based on the Schauder and Banach fixed-point theorems, we establish sufficient conditions that guarantee the existence and uniqueness of solutions to nonlinear impulsive delay differential systems. Finally, several examples are given to illustrate our theoretical results.https://www.mdpi.com/2075-1680/13/12/834delay matrix functionimpulsive delay differential systemsexistence |
| spellingShingle | Yingxia Zhou Mengmeng Li Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems Axioms delay matrix function impulsive delay differential systems existence |
| title | Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems |
| title_full | Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems |
| title_fullStr | Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems |
| title_full_unstemmed | Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems |
| title_short | Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems |
| title_sort | existence and uniqueness of second order impulsive delay differential systems |
| topic | delay matrix function impulsive delay differential systems existence |
| url | https://www.mdpi.com/2075-1680/13/12/834 |
| work_keys_str_mv | AT yingxiazhou existenceanduniquenessofsecondorderimpulsivedelaydifferentialsystems AT mengmengli existenceanduniquenessofsecondorderimpulsivedelaydifferentialsystems |