{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:25:43Z","timestamp":1760228743491,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T00:00:00Z","timestamp":1653264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSP-2022\/167"],"award-info":[{"award-number":["RSP-2022\/167"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we establish oscillation theorems for all solutions to fourth-order neutral differential equations using the Riccati transformation approach and some inequalities. Some new criteria are established that can be used in cases where known theorems fail to apply. The approach followed depends on finding conditions that guarantee the exclusion of positive solutions, and as a result of the symmetry between the positive and negative solutions of the studied equation, we therefore exclude negative solutions. An illustrative example is given.<\/jats:p>","DOI":"10.3390\/sym14051068","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T05:12:27Z","timestamp":1653455547000},"page":"1068","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["New Conditions for Testing the Oscillation of Fourth-Order Differential Equations with Several Delays"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3844-7820","authenticated-orcid":false,"given":"Ali","family":"Muhib","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"},{"name":"Department of Mathematics, Faculty of Education\u2014Al-Nadirah, Ibb University, Ibb P.O. Box 70270, Yemen"}]},{"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, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1167-2430","authenticated-orcid":false,"given":"Sameh S.","family":"Askar","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1971). Functional Differential Equations, in Analytic Theory of Differential Equations, Springer.","DOI":"10.1007\/978-1-4615-9968-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1186\/1687-2770-2014-56","article-title":"Oscillation of fourth-order neutral differential equations with p-Laplacian like operators","volume":"9","author":"Li","year":"2014","journal-title":"Bound. Value Probl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1186\/s13660-021-02595-x","article-title":"On oscillation of second-order noncanonical neutral differential equations","volume":"2021","author":"Muhib","year":"2021","journal-title":"J. Inequal. Appl."},{"key":"ref_4","first-page":"3769","article-title":"Oscillation theorems for higher order neutral differential equations","volume":"219","author":"Baculikova","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"185","DOI":"10.29020\/nybg.ejpam.v13i2.3654","article-title":"Some new oscillation results for fourth-order neutral differential equations","volume":"13","author":"Moaaz","year":"2020","journal-title":"Eur. J. Pure Appl. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.aml.2006.01.003","article-title":"Oscillation behavior of even order neutral differential equations with variable coefficients","volume":"19","author":"Zhang","year":"2006","journal-title":"Appl. Math. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1186\/s13662-019-2060-1","article-title":"On the oscillation of fourth-order delay differential equations","volume":"2019","author":"Grace","year":"2019","journal-title":"Adv. Differ. Equ."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Cesarano, C., and Bazighifan, O. (2019). Oscillation of fourth-order functional differential equations with distributed delay. Axioms, 8.","DOI":"10.3390\/axioms8020061"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"839","DOI":"10.7494\/OpMath.2017.37.6.839","article-title":"Oscillatory and asymptotic behavior of a third order nonlinear neutral differential equation","volume":"37","author":"Graef","year":"2017","journal-title":"Opusc. Math."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Moaaz, O., Awrejcewicz, J., and Muhib, A. (2020). Establishing new criteria for oscillation of odd-order nonlinear differential equations. Mathematics, 8.","DOI":"10.3390\/math8060937"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Moaaz, O., Dassios, I., Muhsin, W., and Muhib, A. (2020). Oscillation Theory for Non-Linear Neutral Delay Differential Equations of Third Order. Appl. Sci., 10.","DOI":"10.3390\/app10144855"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1687-1847-2011-45","article-title":"Oscillation of higher-order quasi-linear neutral differential equations","volume":"2011","author":"Xing","year":"2011","journal-title":"Adv. Differ. Equ."},{"key":"ref_13","first-page":"4403821","article-title":"On the oscillation of even-order nonlinear differential equations with mixed neutral terms","volume":"2021","author":"Kaabar","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5691758","DOI":"10.1155\/2019\/5691758","article-title":"Oscillation criteria for third-order emden-fowler differential equations with unbounded neutral coefficients","volume":"2019","author":"Chatzarakis","year":"2019","journal-title":"Complexity"},{"key":"ref_15","first-page":"1","article-title":"Oscillation results for even-order quasilinear neutral functional differential equations","volume":"2011","author":"Baculikova","year":"2011","journal-title":"Electron. J. Differ. Equ."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","unstructured":"Bazighifan, O., Moaaz, O., El-Nabulsi, R.A., and Muhib, A. (2020). Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument. Symmetry, 12.","DOI":"10.3390\/sym12081248"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.aml.2016.04.012","article-title":"Oscillation criteria for even-order neutral differential equations","volume":"61","author":"Li","year":"2016","journal-title":"Appl. Math. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kiguradze, I.T., and Chanturiya, T.A. (1993). Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-011-1808-8"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.aml.2012.08.004","article-title":"New results for oscillatory behavior of even-order half-linear delay differential equations","volume":"26","author":"Zhang","year":"2013","journal-title":"Appl. Math. Lett."},{"key":"ref_21","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."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1068\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:16:44Z","timestamp":1760138204000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,23]]},"references-count":21,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14051068"],"URL":"https:\/\/doi.org\/10.3390\/sym14051068","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,5,23]]}}}