{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:38Z","timestamp":1760146658687,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12201148","QKHJC-ZK[2022]YB069"],"award-info":[{"award-number":["12201148","QKHJC-ZK[2022]YB069"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["12201148","QKHJC-ZK[2022]YB069"],"award-info":[{"award-number":["12201148","QKHJC-ZK[2022]YB069"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/axioms13120834","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T11:26:08Z","timestamp":1732706768000},"page":"834","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Uniqueness of Second-Order Impulsive Delay Differential Systems"],"prefix":"10.3390","volume":"13","author":[{"given":"Yingxia","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6926-8716","authenticated-orcid":false,"given":"Mengmeng","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"ref_1","first-page":"927","article-title":"Exact solutions and finite time stability of linear conformable fractional systems with pure delay","volume":"134","author":"Elshenhab","year":"2023","journal-title":"CMES Comput. 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