{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:27:36Z","timestamp":1760236056815,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T00:00:00Z","timestamp":1635379200000},"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 work, new sufficient conditions for the oscillation of all solutions of the second-order neutral delay differential equations with the non-canonical operator are established. Using a generalized Riccati substitution, we obtained criteria that complement and extend some previous results in the literature.<\/jats:p>","DOI":"10.3390\/axioms10040281","type":"journal-article","created":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T23:50:28Z","timestamp":1635465028000},"page":"281","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["New Sufficient Conditions for Oscillation of Second-Order Neutral Delay Differential Equations"],"prefix":"10.3390","volume":"10","author":[{"given":"Taher","family":"Hassan","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"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"},{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"}]},{"given":"Amany","family":"Nabih","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"given":"Mouataz","family":"Mesmouli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}]},{"given":"Ahmed","family":"El-Sayed","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21568, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,28]]},"reference":[{"key":"ref_1","unstructured":"El\u2019sgol\u2019c, L.E. (1964). Qualitative Methods in Mathematical Analysis, American Mathematical Society."},{"key":"ref_2","unstructured":"El\u2019sgol\u2019ts, L.E., and Norkin, S.B. (1973). Introduction to the Theory andApplication of Differential Equations with Deviating Arguments, Academic Press, Inc."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gyri, I., and Ladas, G. (1991). Oscillation Theory of Delay Differential Equations, Oxford University Press.","DOI":"10.1093\/oso\/9780198535829.001.0001"},{"key":"ref_4","unstructured":"Erbe, L.H., Kong, Q., and Zhang, B.G. (1995). Oscillation Theory for Functional Differential Equations, Marcel Dekker, Inc."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1977). Functional Differential Equations, Springer.","DOI":"10.1007\/978-1-4612-9892-2"},{"key":"ref_6","first-page":"267","article-title":"Oscillation of second order neutral delay differential equation","volume":"1","author":"Grammatikopoulos","year":"1985","journal-title":"Rad. Math."},{"key":"ref_7","first-page":"77","article-title":"Oscillation of nonlinear second order neutral delay differential equations","volume":"3","author":"Grace","year":"1987","journal-title":"Rad. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1687-1847-2010-763278","article-title":"On the oscillation of second-order neutral delay differential equations","volume":"2010","author":"Han","year":"2010","journal-title":"Adv. Differ. Equ."},{"key":"ref_9","first-page":"2739","article-title":"Oscillation and asymptotic analysis on a new generalized Emden\u2013Fowler equation","volume":"219","author":"Liu","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_10","first-page":"2739","article-title":"Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type","volume":"219","author":"Wu","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4472","DOI":"10.1016\/j.camwa.2011.10.024","article-title":"Oscillation theorems for second-order nonlinear neutral differential equations","volume":"62","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.aml.2021.107172","article-title":"Second-order Emden\u2013Fowler neutral differential equations: A new precise criterion for oscillation","volume":"118","author":"Moaaz","year":"2021","journal-title":"Appl. Math. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.aml.2017.02.003","article-title":"A note on oscillation of second-order delay differential equa tions","volume":"69","year":"2017","journal-title":"Appl. Math. Lett."},{"key":"ref_14","first-page":"404","article-title":"New oscillation criteria for second-order half-linear advanced differential equations","volume":"347","author":"Chatzarakis","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1186\/s13662-020-02626-9","article-title":"Some oscillation theorems for nonlinear second-order differential equations with an advanced argument","volume":"2020","author":"Chatzarakis","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_16","first-page":"178","article-title":"Some remarks on oscillation of second order neutral differential equations","volume":"274","author":"Agarwal","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.14232\/ejqtde.2017.1.60","article-title":"Oscillation criteria for second-order neutral delay differential equations","volume":"2017","author":"Bohner","year":"2017","journal-title":"Electron. J. Qual. Theory Differ. Equ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1186\/s13660-020-02332-w","article-title":"An improved approach for studying oscillation of generalized Emden\u2013Fowler neutral differential equation","volume":"2020","author":"Moaaz","year":"2020","journal-title":"J. Ineq. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Moaaz, O., Anis, M., Baleanu, D., and Muhib, A. (2020). More effective criteria for oscillation of second-order differential equations with neutral arguments. Mathematics, 8.","DOI":"10.3390\/math8060986"},{"key":"ref_20","first-page":"787","article-title":"A new approach in the study of oscillatory behavior of even-order neutral delay differential equations","volume":"225","author":"Agarwal","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"ref_21","first-page":"3769","article-title":"Oscillation theorems for higher order neutral differential equations","volume":"219","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1687-1847-2010-184180","article-title":"Oscillation of even-order neutral delay differential equations","volume":"2010","author":"Li","year":"2010","journal-title":"Adv. Differ. Equ."},{"key":"ref_23","first-page":"181","article-title":"On the oscillation of third-order quasi-linear neutral functional differential equations","volume":"47","author":"Thandapani","year":"2011","journal-title":"Arch. Math."},{"key":"ref_24","first-page":"388","article-title":"Oscillation criteria for second order quasilinear neutral delay differential equations","volume":"207","author":"Ye","year":"2009","journal-title":"Appl. Math. 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