{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:23:21Z","timestamp":1768343001816,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T00:00:00Z","timestamp":1618790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, so our results extend and complement previous results in the literature. Further, we provide two examples to illustrate the main results.<\/jats:p>","DOI":"10.3390\/sym13040722","type":"journal-article","created":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T21:59:49Z","timestamp":1618869589000},"page":"722","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Second-Order Impulsive Delay Differential Systems: Necessary and Sufficient Conditions for Oscillatory or Asymptotic Behavior"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9740-3081","authenticated-orcid":false,"given":"Shyam Sundar","family":"Santra","sequence":"first","affiliation":[{"name":"Department of Mathematics, JIS College of Engineering, Kalyani 741235, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4167-1690","authenticated-orcid":false,"given":"Khaled Mohamed","family":"Khedher","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia"},{"name":"Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-1022","authenticated-orcid":false,"given":"Osama","family":"Moaaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3844-7820","authenticated-orcid":false,"given":"Ali","family":"Muhib","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"},{"name":"Department of Mathematics, Faculty of Education\u2014Al-Nadirah, Ibb University, Ibb 999101, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5280-2975","authenticated-orcid":false,"given":"Shao-Wen","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bainov, D.D., and Simeonov, P.S. 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