{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:23:46Z","timestamp":1760145826839,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:00:00Z","timestamp":1725494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Deanship at University of Ha\u2019il, Saudi Arabia","award":["RG-23 138"],"award-info":[{"award-number":["RG-23 138"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates second-order functional dynamic equations with mixed nonlinearities on an arbitrary unbounded above-time scale, T. We will use a unified time scale approach and the well-known Riccati technique to derive oscillation criteria of the Nehari-type for second-order dynamic equations. The findings demonstrate a significant improvement in the literature on dynamic equations. The symmetry is beneficial and influential in defining the right style of study for the qualitative behavior of solutions to dynamic equations. We include an example to demonstrate the significance of our results.<\/jats:p>","DOI":"10.3390\/sym16091156","type":"journal-article","created":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T02:34:06Z","timestamp":1725503646000},"page":"1156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2907-3353","authenticated-orcid":false,"given":"Taher S.","family":"Hassan","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"},{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8845-3095","authenticated-orcid":false,"given":"Loredana Florentina","family":"Iambor","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sorin","family":"Mure\u015fan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khalid","family":"Alenzi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2434-1929","authenticated-orcid":false,"given":"Ismoil","family":"Odinaev","sequence":"additional","affiliation":[{"name":"Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khudhayr A.","family":"Rashedi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/BF03323153","article-title":"Analysis on measure chains\u2014A unified approach to continuous and discrete calculus","volume":"18","author":"Hilger","year":"1990","journal-title":"Results Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kac, V., and Chueng, P. 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