{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:43:56Z","timestamp":1760402636963,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,2]],"date-time":"2020-05-02T00:00:00Z","timestamp":1588377600000},"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>New sufficient criteria are obtained for the oscillation of a non-autonomous first order differential equation with non-monotone delays. Both recursive and lower-upper limit types criteria are given. The obtained results improve most recent published results. An example is given to illustrate the applicability and strength of our results.<\/jats:p>","DOI":"10.3390\/sym12050718","type":"journal-article","created":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T06:41:20Z","timestamp":1588660880000},"page":"718","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays"],"prefix":"10.3390","volume":"12","author":[{"given":"Emad R.","family":"Attia","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2571-1215","authenticated-orcid":false,"given":"Hassan A.","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Bisha, Bisha 61922, P.O. Box 344, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis P.","family":"Stavroulakis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"},{"name":"Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Agarwal, R.P., Berezansky, L., Braverman, E., and Domoshnitsky, A. (2012). Non-Oscillation Theory of Functional Differential Equations with Applications, Springer.","DOI":"10.1007\/978-1-4614-3455-9"},{"key":"ref_2","first-page":"3880","article-title":"On oscillation of differential and difference equations with non-monotone delays","volume":"218","author":"Braverman","year":"2011","journal-title":"Appl. Math. 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Oscillations of Higher-Order Retarded Differential Equations Generated by the Retarded Arguments, in Delay and Functional Differential Equations and Their Applications, Academic Press.","DOI":"10.1016\/B978-0-12-627250-5.50013-7"},{"key":"ref_14","first-page":"160","article-title":"Linear homogeneous differential equations of first order with deviating arguments","volume":"5","author":"Myshkis","year":"1950","journal-title":"Uspekhi Mat. Nauk"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"207","DOI":"10.4153\/CMB-1998-030-3","article-title":"An oscillation criterion for first-order linear delay differential equations","volume":"41","author":"Philos","year":"1998","journal-title":"Canad. Math. Bull."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1112\/S0024609302001662","article-title":"Oscillation criteria for first-order delay equations","volume":"35","author":"Sficas","year":"2003","journal-title":"Bull. London Math. 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Ekvac."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/5\/718\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:52:22Z","timestamp":1760363542000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/5\/718"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,2]]},"references-count":19,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,5]]}},"alternative-id":["sym12050718"],"URL":"https:\/\/doi.org\/10.3390\/sym12050718","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,5,2]]}}}