{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T06:53:07Z","timestamp":1763621587654,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T00:00:00Z","timestamp":1707004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University Researchers Supporting Project","award":["PNURSP2024R406"],"award-info":[{"award-number":["PNURSP2024R406"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper deals with the oscillatory behavior of solutions of a new class of second-order nonlinear differential equations. In contrast to most of the previous results in the literature, we establish some new criteria that guarantee the oscillation of all solutions of the studied equation without additional restrictions. Our approach improves the standard integral averaging technique to obtain simpler oscillation theorems for new classes of nonlinear differential equations. Two examples are presented to illustrate the importance of our findings.<\/jats:p>","DOI":"10.3390\/axioms13020105","type":"journal-article","created":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T03:28:29Z","timestamp":1707103709000},"page":"105","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 Solutions of Second-Order Nonlinear Differential Equations with Damped Term"],"prefix":"10.3390","volume":"13","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\/0000-0003-2791-6230","authenticated-orcid":false,"given":"Higinio","family":"Ramos","sequence":"additional","affiliation":[{"name":"Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain"},{"name":"Department of Mathematics, Escuela Politecnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,4]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","unstructured":"Aldiaiji, M., Qaraad, B., Iambor, L.F., and Elabbasy, E.M. (2023). New Oscillation Theorems for Second-Order Superlinear Neutral Differential Equations with Variable Damping Terms. Symmetry, 15.","DOI":"10.3390\/sym15091630"},{"key":"ref_3","first-page":"106","article-title":"Memoire sur les equations differentielles lineaires du second ordre","volume":"1","author":"Sturm","year":"1836","journal-title":"J. Math. Pures Appl."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1971). Analytic Theory of Differential Equations, Springer.","DOI":"10.1007\/978-1-4615-9968-5"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Cesarano, C., Moaaz, O., Qaraad, B., Alshehri, N.A., Elagan, S.K., and Zakarya, M. (2021). New Results for Oscillation of Solutions of Odd-Order NeutralDifferential Equations. Symmetry, 13.","DOI":"10.3390\/sym13061095"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","unstructured":"Berezansky, L., Domoshnitsky, A., and Koplatadze, R. (2020). Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations, CRC Press.","DOI":"10.1201\/9780429321689"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1186\/s13660-018-1767-y","article-title":"An improved approach for studying oscillation of second-order neutral delay differential equations","volume":"2018","author":"Grace","year":"2018","journal-title":"J. Inequal. Appl."},{"key":"ref_9","unstructured":"Erbe, L., Kong, Q., and Zhang, B.G. (1994). Oscillation Theory for Functional Differential Equations, CRC Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5257","DOI":"10.1016\/j.cma.2005.09.027","article-title":"Isogeometric analysis of structural vibrations","volume":"195","author":"Cottrell","year":"2006","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1007\/s11831-018-9295-y","article-title":"Symbol based analysis of fiinite 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_12","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.cma.2016.05.042","article-title":"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. Engrg."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1186\/s13660-016-1246-2","article-title":"Asymptotic behavior of even-order damped differential equations with p-Laplacian like operators and deviating arguments","volume":"2016","author":"Liu","year":"2016","journal-title":"J. Inequal. Appl."},{"key":"ref_14","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_15","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. Analy. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ioannis, D., Muhib, A., El-Marouf, S.A., and Elagan, S.K. (2023). Oscillation of Neutral Differential Equations with Damping Terms. Mathematics, 11.","DOI":"10.3390\/math11020447"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wu, Y., Yu, Y., and Xiao, J. (2022). Oscillation of Second Order Nonlinear Neutral Differential Equations. Mathematics, 10.","DOI":"10.3390\/math10152739"},{"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. Inequal. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1002\/mana.19891410114","article-title":"Oscillation theorems for second order nonlinear differential equations with damping","volume":"141","author":"Grace","year":"1989","journal-title":"Math. Nachr."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"759","DOI":"10.18514\/MMN.2017.2326","article-title":"Oscillatory behavior of second order damped neutral differential equations with distributed deviating arguments","volume":"18","author":"Grace","year":"2017","journal-title":"Miskolc Math. Notes"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF01848010","article-title":"Oscillations in second order differential equations with alternating coefficients, Period","volume":"19","author":"Grace","year":"1988","journal-title":"Math. Hungar."},{"key":"ref_22","unstructured":"Grace, S.R., and Jadlovska, I. (2017). Dynamical Systems\u2014Analytical and Computational Techniques, IntechOpen."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1006\/jmaa.2000.6975","article-title":"Oscillation results for a second order damped differential equation with nonmonotonous nonlinearity","volume":"250","author":"Kirane","year":"2000","journal-title":"J. Math. Anal. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.na.2007.05.012","article-title":"Oscillation criteria for second-order nonlinear differential equations with damping","volume":"69","author":"Rogovchenko","year":"2008","journal-title":"Nonlinear Anal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2191","DOI":"10.1016\/j.camwa.2010.09.011","article-title":"Oscillation of even-order half-linear functional differential equations with damping","volume":"61","author":"Liu","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1016\/j.jmaa.2006.02.021","article-title":"Oscillation criteria for second-order damped nonlinear differential equations with p-Laplacian","volume":"325","author":"Yamaoka","year":"2007","journal-title":"J. Math. Anal. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1016\/j.aml.2011.04.025","article-title":"Oscillation criteria for even-order half-linear functional differential equations with damping","volume":"24","author":"Zhang","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1016\/S0362-546X(98)00324-1","article-title":"Oscillation theorems for second-order equations with damping","volume":"41","author":"Rogovchenko","year":"2000","journal-title":"Nonlinear Anal."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/0022-247X(92)90386-R","article-title":"Oscillation theorems for nonlinear differential equations of second order","volume":"171","author":"Grace","year":"1992","journal-title":"J. Math. Anal. Appl."},{"key":"ref_30","first-page":"1","article-title":"Oscillation of second-order nonlinear differential equations with a damping term","volume":"76","author":"Elabbasy","year":"2005","journal-title":"Electron. J. Differ. Equ."},{"key":"ref_31","first-page":"177","article-title":"On oscillation of nonlinear second order differential equation with damping term","volume":"117","author":"Kirane","year":"2001","journal-title":"Appl. Math. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/S0898-1221(00)00155-3","article-title":"Interval oscillation criteria for second order nonlinear differential equations with damping","volume":"40","author":"Li","year":"2000","journal-title":"Comput. Math. Appl."},{"key":"ref_33","first-page":"531","article-title":"Oscillation of second order nonlinear neutral differential equations","volume":"135","author":"Jiang","year":"2003","journal-title":"Appl. Math. Comput."},{"key":"ref_34","unstructured":"Hardy, G.H., Littlewood, J.E., and Polya, G. (1988). Inequalities, Cambridge University Press. [2nd ed.]."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0022-247X(90)90301-U","article-title":"Integral averaging technique for the oscillation of second order nonlinear differential equations","volume":"149","author":"Grace","year":"1990","journal-title":"J. Math. Anal. Appl."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/2\/105\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:54:38Z","timestamp":1760104478000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/2\/105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,4]]},"references-count":35,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["axioms13020105"],"URL":"https:\/\/doi.org\/10.3390\/axioms13020105","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,2,4]]}}}