{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:16:21Z","timestamp":1760235381895,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"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>The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(\u03b9)[(b(\u03b9)x(\u03b9)+p(\u03b9)x(\u03b9\u2212\u03c4)\u2032)\u2032]\u03b2)\u2032+\u222bcdq(\u03b9,\u03bc)x\u03b2(\u03c3(\u03b9,\u03bc))d\u03bc=0, where \u03b9\u2265\u03b90 and w(\u03b9):=x(\u03b9)+p(\u03b9)x(\u03b9\u2212\u03c4). New oscillation results are established by using the generalized Riccati technique under the assumption of \u222b\u03b90\u03b9a\u22121\/\u03b2(s)ds&lt;\u222b\u03b90\u03b91b(s)ds=\u221eas\u03b9\u2192\u221e. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.<\/jats:p>","DOI":"10.3390\/axioms10030192","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T10:54:35Z","timestamp":1629284075000},"page":"192","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Oscillation and Asymptotic Properties of Differential Equations of Third-Order"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5786-1309","authenticated-orcid":false,"given":"R.","family":"Elayaraja","sequence":"first","affiliation":[{"name":"Department of Mathematics, Annai Mathammal Sheela Engineering College, Namakkal 637013, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"Ganesan","sequence":"additional","affiliation":[{"name":"PG and Research Department of Mathematics, Aringar Anna Government Arts College, Namakkal 637002, Tamil Nnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-9608","authenticated-orcid":false,"given":"Omar","family":"Bazighifan","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Rome, Italy"},{"name":"Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hale, J.K. 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