{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:42:17Z","timestamp":1767109337308,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T00:00:00Z","timestamp":1675728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2023R216"],"award-info":[{"award-number":["PNURSP2023R216"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study aims to investigate the asymptotic behavior of a class of third-order delay differential equations. Here, we consider an equation with a middle term and several delays. We obtain an iterative relationship between the positive solution of the studied equation and the corresponding function. Using this new relationship, we derive new criteria that ensure that all non-oscillatory solutions converge to zero. The new findings are an extension and expansion of relevant findings in the literature. We apply our results to a special case of the equation under study to clarify the importance of the new criteria.<\/jats:p>","DOI":"10.3390\/axioms12020166","type":"journal-article","created":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T02:28:17Z","timestamp":1675736897000},"page":"166","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Third-Order Neutral Differential Equation with a Middle Term and Several Delays: Asymptotic Behavior of Solutions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2878-5300","authenticated-orcid":false,"given":"Barakah","family":"Almarri","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-1022","authenticated-orcid":false,"given":"Osama","family":"Moaaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"given":"Mona","family":"Anis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"given":"Belgees","family":"Qaraad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1971). 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