{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:24:42Z","timestamp":1762957482185,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T00:00:00Z","timestamp":1718582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, a survey of the most interesting conditions for the oscillation of all solutions to first-order linear differential equations with a retarded argument is presented in chronological order, especially in the case when well-known oscillation conditions are not satisfied. The essential improvement and the importance of these oscillation conditions is also indicated.<\/jats:p>","DOI":"10.3390\/axioms13060407","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T11:14:16Z","timestamp":1718622856000},"page":"407","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Survey on the Oscillation of First-Order Retarded Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"given":"Ioannis P.","family":"Stavroulakis","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,17]]},"reference":[{"key":"ref_1","unstructured":"Erbe, L.H., Kong, Q., and Zhang, B.G. (1995). 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Symmetry, 12.","DOI":"10.3390\/sym12050718"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1515\/gmj-2019-2055","article-title":"Oscillation of first order differential equations with several non-monotone retarded arguments","volume":"27","author":"Bereketoglu","year":"2020","journal-title":"Georgian Math. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4017","DOI":"10.1090\/S0002-9939-2011-10820-7","article-title":"On some constants for oscillation and stability of delay equations","volume":"139","author":"Berezansky","year":"2011","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_8","first-page":"766","article-title":"On oscillation of differential and difference equations with non-monotone delays","volume":"58","author":"Braverman","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_9","first-page":"1","article-title":"Oscillation tests for differential equations with deviating arguments","volume":"27","author":"Chatzarakis","year":"2018","journal-title":"Adv. Math. Sci. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Elbert, A., and Stavroulakis, I.P. (1992). Oscillations of first order differential equations with deviating arguments. Recent Trends in Differential Equations, World Sci. Publishing Co.","DOI":"10.1142\/9789812798893_0013"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.1090\/S0002-9939-1995-1242082-1","article-title":"Oscillation and non-oscillation criteria for delay differential equations","volume":"123","author":"Elbert","year":"1995","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.aml.2015.10.014","article-title":"New oscillation criterion for delay differential equations with non-monotone arguments","volume":"54","author":"Attia","year":"2016","journal-title":"Appl. Math. Lett."},{"key":"ref_13","first-page":"305","article-title":"Oscillation of first order linear differential equations with deviating arguments","volume":"1","author":"Erbe","year":"1988","journal-title":"Differ. Integral Equ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/BF01773379","article-title":"Oscillation theory of first order functional differential equations with deviating arguments","volume":"136","author":"Fukagai","year":"1984","journal-title":"Ann. Mat. Pura Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1619\/fesi.58.347","article-title":"Oscillation criteria for differential equations with several retarded arguments","volume":"58","author":"Infante","year":"2015","journal-title":"Funkc. Ekvac."},{"key":"ref_16","first-page":"139","article-title":"Oscillation tests for delay equations","volume":"29","author":"Stavroulakis","year":"1999","journal-title":"Rocky Mt. J. Math."},{"key":"ref_17","first-page":"32","article-title":"Oscillation of linear differential equations with deviating argument","volume":"1","author":"Jian","year":"1991","journal-title":"Math. Pract. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2989","DOI":"10.1090\/S0002-9939-00-05530-1","article-title":"Oscillation criteria for delay equations","volume":"128","author":"Kon","year":"2000","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_19","first-page":"1463","article-title":"On the oscillatory and monotonic solutions of first order differential equations with deviating arguments","volume":"18","author":"Koplatadze","year":"1982","journal-title":"Differ. Uravn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1007\/BF02254685","article-title":"On the oscillation of solutions of first order delay differential inequalities and equations","volume":"1","author":"Koplatadze","year":"1994","journal-title":"Georgian Math. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/0022-247X(91)90396-H","article-title":"Oscillation of first order delay equations","volume":"156","author":"Kwong","year":"1991","journal-title":"J. Math. Anal. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1080\/00036817908839256","article-title":"Sharp conditions for oscillations caused by delay","volume":"9","author":"Ladas","year":"1979","journal-title":"Appl. Anal."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ladas, G., Laskhmikantham, V., and Papadakis, J.S. (1972). Oscillations of higher-order retarded differential equations generated by retarded arguments. Delay and Functional Differential Equations and Their Applications, Academic Press.","DOI":"10.1016\/B978-0-12-627250-5.50013-7"},{"key":"ref_24","first-page":"105","article-title":"On delay differential inequalities of first order","volume":"25","author":"Ladas","year":"1982","journal-title":"Funkc. Ekvac."},{"key":"ref_25","unstructured":"Ladde, G.S., Lakshmikantham, V., and Zhang, B.G. (1987). Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3729","DOI":"10.1090\/S0002-9939-96-03674-X","article-title":"Oscillations of first order delay differential equations","volume":"124","author":"Li","year":"1996","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_27","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_28","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_29","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. Lond. Math. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.amc.2013.10.041","article-title":"Oscillation criteria for delay and difference equations with non-monotone arguments","volume":"226","author":"Stavroulakis","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_31","first-page":"171","article-title":"A Survey on the oscillation of solutions of first order linear differential equations with deviating arguments","volume":"2","author":"Wang","year":"2002","journal-title":"Appl. Math. E-Notes"},{"key":"ref_32","first-page":"59","article-title":"Oscillations of differential equations with deviating arguments","volume":"2","author":"Yu","year":"1992","journal-title":"Pan-Am. Math. J."},{"key":"ref_33","first-page":"434","article-title":"On some problems on oscillation of functional differential equations of first order","volume":"25","author":"Zhou","year":"1990","journal-title":"J. Shandong Univ."},{"key":"ref_34","first-page":"288","article-title":"On the oscillation of solutions of first order differential equations with deviating arguments","volume":"15","author":"Zhou","year":"1999","journal-title":"Acta Math. Appl. 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