{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T15:48:28Z","timestamp":1765295308315,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,13]],"date-time":"2022-03-13T00:00:00Z","timestamp":1647129600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main purpose of this research was to use the comparison approach with a first-order equation to derive criteria for non-oscillatory solutions of fourth-order nonlinear neutral differential equations with p Laplacian operators. We obtained new results for the behavior of solutions to these equations, and we showed their symmetric and non-oscillatory characteristics. These results complement some previously published articles. To find out the effectiveness of these results and validate the proposed work, two examples were discussed at the end of the paper.<\/jats:p>","DOI":"10.3390\/sym14030566","type":"journal-article","created":{"date-parts":[[2022,3,13]],"date-time":"2022-03-13T21:44:17Z","timestamp":1647207857000},"page":"566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Symmetric and Non-Oscillatory Characteristics of the Neutral Differential Equations Solutions Related to p-Laplacian Operators"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2878-5300","authenticated-orcid":false,"given":"Barakah","family":"Almarri","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2959-4212","authenticated-orcid":false,"given":"Ali Hasan","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq"},{"name":"Doctoral School of Mathematical and Computational Sciences, University of Debrecen, H-4002 Debrecen, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4392-0742","authenticated-orcid":false,"given":"Khalil S.","family":"Al-Ghafri","sequence":"additional","affiliation":[{"name":"University of Technology and Applied Sciences, P.O. Box 14, Ibri 516, Oman"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0939-7564","authenticated-orcid":false,"given":"Alanoud","family":"Almutairi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Hafr Al Batin, P.O. Box 1803, Hafar Al Batin 31991, Saudi Arabia"}]},{"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 Roma, Italy"},{"name":"Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0387-921X","authenticated-orcid":false,"given":"Jan","family":"Awrejcewicz","sequence":"additional","affiliation":[{"name":"Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1\/15 Stefanowski Str., 90-924 Lodz, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,13]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1186\/s13662-017-1353-5","article-title":"Oscillations of differential equations generated by several deviating arguments","volume":"2017","author":"Chatzarakis","year":"2017","journal-title":"Adv. Differ. Equ."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bazighifan, O., and Dassios, I. (2020). Riccati Technique and Asymptotic Behavior of Fourth-Order Advanced Differential Equations. Mathematics, 8.","DOI":"10.3390\/math8040590"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8237634","DOI":"10.1155\/2018\/8237634","article-title":"Oscillation criteria for delay and advanced differential equations with nonmonotone arguments","volume":"2018","author":"Chatzarakis","year":"2018","journal-title":"Complexity"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Elabbasy, E.M., Cesarano, C., Bazighifan, O., and Moaaz, O. (2019). Asymptotic and oscillatory behavior of solutions of a class of higher order differential equation. Symmetry, 11.","DOI":"10.3390\/sym11121434"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"763278","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_8","doi-asserted-by":"crossref","unstructured":"Kiguradze, I.T., and Chanturiya, T.A. (1993). A Symptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Kluwer Acad. Publ.","DOI":"10.1007\/978-94-011-1808-8"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Agarwal, R.P., Bazighifan, O., and Ragusa, M.A. (2021). Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions. Entropy, 23.","DOI":"10.3390\/e23020129"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1186\/s13662-019-2240-z","article-title":"Oscillation criteria for even-order neutral differential equations with distributed deviating arguments","volume":"2019","author":"Moaaz","year":"2019","journal-title":"Adv. Differ. Equ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1515\/dema-2013-0444","article-title":"Oscillation of higher-order half-linear neutral differential equations","volume":"1","author":"Tang","year":"2013","journal-title":"Demonstr. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"45","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","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0893-9659(98)00028-7","article-title":"Oscillation criteria for even order neutral differential equations","volume":"11","author":"Zafer","year":"1998","journal-title":"Appl. Math. Lett."},{"key":"ref_14","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_15","first-page":"243","article-title":"Asymptotic Solutions of Fifth Order Overdamped-Oscillatory Nonlinear Systems","volume":"1","author":"Roshid","year":"2020","journal-title":"Contemp. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"105867","DOI":"10.1016\/j.cnsns.2021.105867","article-title":"Breather, multi-shock waves and localized excitation structure solutions to the Extended BKP\u2013Boussinesq equation","volume":"101","author":"Roshid","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_17","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":"2014","author":"Li","year":"2014","journal-title":"Bound. Value Probl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1016\/j.jmaa.2013.07.066","article-title":"Oscillation and asymptotic behavior of higher-order delay differential equations with p-Laplacian like operators","volume":"409","author":"Zhang","year":"2014","journal-title":"J. Math. Anal. Appl."},{"key":"ref_19","first-page":"125475","article-title":"On the oscillation of certain fourth-order differential equations with p-Laplacian like operator","volume":"386","author":"Bazighifan","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bazighifan, O., Ghanim, F., Awrejcewicz, J., Al-Ghafri, K.S., and Al-Kandari, M. (2021). New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-like Operators. Mathematics, 9.","DOI":"10.3390\/math9202584"},{"key":"ref_21","first-page":"787","article-title":"A new approach in the study of oscillatory behavior of even-order neutral delay diferential equations","volume":"225","author":"Agarwal","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Agarwal, R., Grace, S., and O\u2019Regan, D. (2000). Oscillation Theory for Difference and Functional Differential Equations, Kluwer Acad. Publ.","DOI":"10.1007\/978-94-015-9401-1"},{"key":"ref_23","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_24","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_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0895-7177(97)00141-6","article-title":"Oscillation criteria for second order retarded differential equations","volume":"26","author":"Agarwal","year":"1997","journal-title":"Math. Comput. Model."},{"key":"ref_26","first-page":"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_27","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1090\/S0002-9939-1980-0548086-5","article-title":"Oscillation of first-order nonlinear differential equations with deviating arguments","volume":"78","author":"Kitamura","year":"1980","journal-title":"Proc. Am. Math. Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/566\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:35:48Z","timestamp":1760135748000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/566"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,13]]},"references-count":27,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["sym14030566"],"URL":"https:\/\/doi.org\/10.3390\/sym14030566","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,3,13]]}}}