{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T00:23:19Z","timestamp":1773966199340,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T00:00:00Z","timestamp":1708560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European High-Performance Computing Joint Undertaking (JU)","award":["955701"],"award-info":[{"award-number":["955701"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the current paper, we aim to study the oscillatory behavior of a new class of third-order differential equations. In the present study, we are interested in a better understanding of the relationships between the solutions and their derivatives. The recursive nature of these relationships enables us to obtain new criteria that ensure the oscillation of all solutions of the studied equation. In comparison with previous studies, our results are more general and include models in a wider range of applications. Furthermore, our findings are also significant because no additional restrictive conditions are required. The presented examples illustrate the significance of the results.<\/jats:p>","DOI":"10.3390\/axioms13030139","type":"journal-article","created":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T03:30:26Z","timestamp":1708572626000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["More Effective Criteria for Testing the Oscillation of Solutions of Third-Order Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"given":"Najiyah","family":"Omar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"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, SE-751 05 Uppsala, Sweden"}]},{"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"}]},{"given":"Faizah","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Sciences, Umm Al-Quraa University, Makkah 24227, 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"}]},{"given":"Elmetwally M.","family":"Elabbasy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,22]]},"reference":[{"key":"ref_1","unstructured":"Strikwerda, J.C. (1989). Finite Difference Schemes and Partial Differential Equations, Chapman and Hall."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ciarlet, P. (1978). The Finite Element Method for Elliptic Problems, North Holland.","DOI":"10.1115\/1.3424474"},{"key":"ref_3","unstructured":"Versteeg, H.K., and Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cottrell, J.A., Hughes, T.J.R., and Bazilevs, Y. (2009). Isogeometric Analysis: Toward integration of CAD and FEA, John Wiley & Sons.","DOI":"10.1002\/9780470749081"},{"key":"ref_5","unstructured":"B\u00f6ttcher, A., and Silbermann, B. (2012). Introduction to Large Truncated Toeplitz Matrices, Springer Science & Business Media."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Garoni, C., and Serra-Capizzano, S. (2018). The Theory of Generalized Locally Toeplitz Sequences: Theory and Applications\u2014Vol II, Springer. Springer Monographs in Mathematics.","DOI":"10.1007\/978-3-030-02233-4"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1007\/s11831-018-9295-y","article-title":"Symbol-based analysis of finite element and isogeometric B-spline discretizations of eigenvalue problems: Exposition and review","volume":"26","author":"Garoni","year":"2019","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.cma.2016.05.042","article-title":"Stefano Spectral analysis of coupled PDEs and of their Schur complements via generalized locally Toeplitz sequences in 2D","volume":"309","author":"Dorostkar","year":"2016","journal-title":"Comput. Methods Appl. Mech. Engrgy"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kiguradze, I.T., and Chanturia, T.A. (1993). Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Springer.","DOI":"10.1007\/978-94-011-1808-8"},{"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. Symmetry, 11.","DOI":"10.3390\/math11122605"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13662-017-1384-y","article-title":"Oscillation criteria for third-order delay differential equations","volume":"2017","author":"Chatzarakis","year":"2017","journal-title":"Adv. Differ. Equ."},{"key":"ref_12","unstructured":"Saker, S. (2010). Oscillation Theory of Delay Differential and Difference Equations: Second and Third-Orders, LAP Lambert Academic Publishing."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Padhi, S., and Pati, S. (2014). Theory of Third-Order Differential Equations, Springer.","DOI":"10.1007\/978-81-322-1614-8"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Al Themairi, A., Qaraad, B., Bazighifan, O., and Nonlaopon, K. (2022). Third-Order Neutral Differential Equations with Damping and Distributed Delay: New Asymptotic Properties of Solutions. Symmetry, 14.","DOI":"10.3390\/sym14102192"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"545","DOI":"10.11650\/tjm.17.2013.2095","article-title":"Oscillation of third-order nonlinear delay differential equations","volume":"17","author":"Agarwal","year":"2013","journal-title":"Taiwan J. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1016\/j.aml.2010.03.003","article-title":"Oscillation criteria for third-order nonlinear functional differential equations","volume":"23","author":"Tiryaki","year":"2010","journal-title":"Appl. Math. Lett."},{"key":"ref_17","first-page":"19","article-title":"Neutral differential equations with distribution deviating arguments: Oscillation conditions","volume":"21","author":"Qaraad","year":"2022","journal-title":"J. Ocean Eng. Sci."},{"key":"ref_18","unstructured":"Cecchi, M., Do\u0161l\u00e1, Z., and Marini, M. (2000). Disconjugate operators and related differential equations. Electron J. Qual. Theory Differ. Equ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1023\/A:1022878804065","article-title":"Some properties of third order differential operators","volume":"47","author":"Cecchi","year":"1997","journal-title":"Czechoslov. Math. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0169-5983(86)90013-4","article-title":"Entry flow into a circular tube of slowly varying cross-section","volume":"1","author":"Jayaraman","year":"1986","journal-title":"Fluid Dyn. Res."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Al Themairi, A., Qaraad, B., Bazighifan, O., and Nonlaopon, K. (2022). Third-Order New Conditions for Testing the Oscillation of Third-Order Differential Equations with Distributed Arguments. Symmetry, 14.","DOI":"10.3390\/sym14112416"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"295","DOI":"10.13182\/NSE70-A21219","article-title":"Phase space analysis of reactor kinetics","volume":"42","author":"Vreeke","year":"1970","journal-title":"Nucl. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"23800","DOI":"10.3934\/math.20231212","article-title":"Asymptotic behavior of solutions of the third-order nonlinear advanced differential equations","volume":"8","author":"Qaraad","year":"2023","journal-title":"AIMS Mathematics"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gyori, I., and Ladas, G. (1991). Oscillation Theory of Differential Equations with Applications, Clarendon Press.","DOI":"10.1093\/oso\/9780198535829.001.0001"},{"key":"ref_25","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.","DOI":"10.1007\/978-94-015-9401-1"},{"key":"ref_26","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 delay","volume":"36","author":"Philos","year":"1981","journal-title":"Arch. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"225","DOI":"10.21136\/MB.2010.140700","article-title":"On the oscillation of certain class of third-order nonlinear delay differential equations","volume":"135","author":"Saker","year":"2010","journal-title":"Math. Bohem."},{"key":"ref_28","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_29","doi-asserted-by":"crossref","first-page":"569201","DOI":"10.1155\/2012\/569201","article-title":"Oscillation of third-order neutral delay differential equations","volume":"2012","author":"Li","year":"2012","journal-title":"Abstr. Appl. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1618","DOI":"10.1016\/j.aml.2011.04.015","article-title":"On the oscillation of higher-order half-linear delay differential equations","volume":"24","author":"Zhang","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_31","first-page":"1","article-title":"Oscillation of third-order functional differential equations","volume":"2010","author":"Dzurina","year":"2010","journal-title":"Electron. J. Qual. Theory Differ. Equ."},{"key":"ref_32","first-page":"102","article-title":"On the oscillation of certain third order nonlinear functional differential equations","volume":"202","author":"Grace","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_33","first-page":"117","article-title":"On the oscillation of third-order quasi-linear delay differential equations","volume":"48","author":"Li","year":"2011","journal-title":"Tatra Mt. Math. Publ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.aml.2010.10.043","article-title":"Oscillation of third-order nonlinear differential equations","volume":"24","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_35","unstructured":"Ladde, G.S., Lakshmikantham, V., and Zhang, B.G. (1987). Oscillation Theory of Differential Equations with Deviating Arguments, M. Dekker."},{"key":"ref_36","first-page":"7023","article-title":"Oscillation of third order trinomial delay differential equations","volume":"218","author":"Rogovchenko","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"485","DOI":"10.7494\/OpMath.2015.35.4.485","article-title":"Oscillation criteria for third order nonlinear delay differential equations with damping","volume":"35","author":"Grace","year":"2015","journal-title":"Opusc. Math."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.14232\/ejqtde.2012.1.5","article-title":"Oscillation criteria for third order delay nonlinear differential equations","volume":"2012","author":"Elabbasy","year":"2012","journal-title":"Electron. J. Qual. Theory Differ. Equ."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/139\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:02:54Z","timestamp":1760104974000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,22]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["axioms13030139"],"URL":"https:\/\/doi.org\/10.3390\/axioms13030139","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,22]]}}}