{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:13:24Z","timestamp":1760145204100,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,29]],"date-time":"2024-06-29T00:00:00Z","timestamp":1719619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2024R406"],"award-info":[{"award-number":["PNURSP2024R406"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The present paper studies the asymptotic and oscillatory properties of solutions of odd-order differential equations with advanced arguments and in a noncanonical case. By providing new and effective relationships between the corresponding function and the solution, we present strict and new criteria for testing whether the studied equation exhibits oscillatory behavior or converges to zero. Our results contribute uniquely to oscillation theory by presenting some theorems that improve and expand upon the results found in the existing literature. We also provide an example to corroborate the validity of our proposed criteria.<\/jats:p>","DOI":"10.3390\/sym16070817","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T04:23:43Z","timestamp":1719980623000},"page":"817","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New Monotonic Properties for Solutions of Odd-Order Advanced Nonlinear Differential Equations"],"prefix":"10.3390","volume":"16","author":[{"given":"Asma","family":"Al-Jaser","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2115-0791","authenticated-orcid":false,"given":"Belgees","family":"Qaraad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6265-9925","authenticated-orcid":false,"given":"Faizah","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 24227, Saudi Arabia"}]},{"given":"Stefano","family":"Serra-Capizzano","sequence":"additional","affiliation":[{"name":"Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy"},{"name":"Division of Scientific Computing, Department of Information Technology, Uppsala University, L\u00e4gerhyddsv 2, Hus 2, P.O. Box 337, SE-751 05 Uppsala, Sweden"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1971). Functional differential equations. Oxford Applied Mathematical Sciences, Springer.","DOI":"10.1007\/978-1-4615-9968-5"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Rihan, F.A. (2021). Delay Differential Equations and Applications to Biology, Springer Nature Singapore Pte Ltd.","DOI":"10.1007\/978-981-16-0626-7"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Themairi, A., Qaraad, B., Bazighifan, O., and Nonlaopon, K. (2022). New Conditions for Testing the Oscillation of Third-Order Differential Equations with Distributed Arguments. Symmetry, 14.","DOI":"10.3390\/sym14112416"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1977). Theory of Functional Differential Equations, Springer.","DOI":"10.1007\/978-1-4612-9892-2"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gy\u00f6ri, I., and Ladas, G. (1991). Oscillation Theory of Delay Differential Equations: With Applications, Oxford University Press.","DOI":"10.1093\/oso\/9780198535829.001.0001"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s12346-022-00715-6","article-title":"Asymptotic and Oscillatory Behaviour of Third Order Non-Linear Differential Equations with Canonical Operator and Mixed Neutral Terms","volume":"22","author":"Alzabut","year":"2022","journal-title":"Qual. Theory Dyn. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Agarwal, R.P., Martin, B., and Wan-Tong, L. (2004). Nonoscillation and Oscillation Theory for Functional Differential Equations. Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker.","DOI":"10.1201\/9780203025741"},{"key":"ref_8","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","author":"Baculikova","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"ref_9","first-page":"715","article-title":"Some oscillation results for second-order neutral dynamic equations","volume":"41","author":"Li","year":"2012","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Al-Jaser, A., Qaraad, B., Bazighifan, O., and Iambor, L.F. (2023). Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior. Mathematics, 11.","DOI":"10.3390\/math11122605"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1006\/jmaa.2000.7063","article-title":"Necessary and suffcient conditions for oscillation of second order neutral differential equations","volume":"252","author":"Wong","year":"2000","journal-title":"J. Math. Anal. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s00605-017-1039-9","article-title":"Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations","volume":"184","author":"Li","year":"2017","journal-title":"Monatsh. Math."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Elabbasy, E.M., Qaraad, B., Abdeljawad, T., and Moaaz, O. (2020). Oscillation Criteria for a Class of Third-Order Damped Neutral Differential Equations. Symmetry, 12.","DOI":"10.3390\/sym12121988"},{"key":"ref_14","first-page":"213","article-title":"Oscillatory behavior of second-order half-linear neutral differential equations with damping","volume":"14","author":"Tunc","year":"2019","journal-title":"Adv. Dyn. Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Aldiaiji, M., Qaraad, B., Iambor, L.F., and Elabbasy, E.M. (2023). On the Asymptotic Behavior of Class of Third-Order Neutral Differential Equations with Symmetrical and Advanced Argument. Symmetry, 15.","DOI":"10.3390\/sym15061165"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Bazighifan, O., Ali, A.H., Mofarreh, F., and Raffoul, Y.N. (2022). Extended Approach to the Asymptotic Behavior and Symmetric Solutions of Advanced Differential Equations. Symmetry, 14.","DOI":"10.3390\/sym14040686"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bazighifan, O., Almutairi, A., Almarri, B., and Marin, M. (2021). An Oscillation Criterion of Nonlinear Differential Equations with Advanced Term. Symmetry, 13.","DOI":"10.3390\/sym13050843"},{"key":"ref_18","first-page":"7","article-title":"Oscillation of noncanonical second-order advanced differential equations via canonical transform","volume":"5","author":"Bohner","year":"2022","journal-title":"Constr. Math. Anal."},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10958-014-1701-x","article-title":"Oscillation Criteria for Higher order Nonlinear Functional Differential Equations with Advanced Argument","volume":"197","author":"Koplatadze","year":"2014","journal-title":"J. Math. Sci."},{"key":"ref_21","first-page":"1","article-title":"On the oscillation of odd order advanced differential equations","volume":"214","year":"2014","journal-title":"Bound. Value Probl."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Agarwal, R.P., Grace, S.R., and O\u2019Regan, D. (2000). Oscillation Theory for Difference and Functional Differential Equations, Springer Science and Business Media.","DOI":"10.1007\/978-94-015-9401-1"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1006\/jmaa.2001.7571","article-title":"Oscillation criteria for certain nth order differential equations with deviating arguments","volume":"262","author":"Agarwal","year":"2001","journal-title":"J. Math. Anal. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1618","DOI":"10.1016\/j.aml.2011.04.015","article-title":"On the oscillation of higherorder half-linear delay differential equations","volume":"24","author":"Zhang","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_25","unstructured":"Yao, J., Zhang, X., and Yu, J. (2020). New oscillation criteria for third-order half-linear advanced differential equations. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"339","DOI":"10.2478\/s12175-014-0208-8","article-title":"Property (A) of third-order advanced differential equations","volume":"64","author":"Dzurina","year":"2014","journal-title":"Math. Slovaca"},{"key":"ref_27","first-page":"491","article-title":"On the oscillation of third order functional differential equations","volume":"39","author":"Grace","year":"2008","journal-title":"Indian J. Pure Appl. Math"},{"key":"ref_28","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_29","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1007\/BF01223686","article-title":"On the existence of nonoscillatory solutions tending to zero at \u221e for differential equations with positive delays","volume":"36","author":"Philos","year":"1981","journal-title":"Arch. Math."},{"key":"ref_30","unstructured":"Erbe, L., Kong, Q., and Zhang, B. (1995). Oscillation Theory for Functional Differential Equations, Marcel Dekker."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1112\/S0024610701002678","article-title":"Oscillation for first order superlinear delay differential equations","volume":"65","author":"Tang","year":"2002","journal-title":"J. Lond. Math. Soc."},{"key":"ref_32","first-page":"1","article-title":"Properties of third order nonlinear functional differential equations with mixed arguments","volume":"2011","year":"2011","journal-title":"Abstr. Appl. Anal."},{"key":"ref_33","unstructured":"Ladde, G.S., Lakshmikantham, V., and Zhang, B.G. (1987). Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/7\/817\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:07:38Z","timestamp":1760108858000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/7\/817"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,29]]},"references-count":33,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["sym16070817"],"URL":"https:\/\/doi.org\/10.3390\/sym16070817","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,6,29]]}}}