{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T08:41:24Z","timestamp":1767084084649,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,2,25]],"date-time":"2021-02-25T00:00:00Z","timestamp":1614211200000},"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 oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form p(\u03b9)w\u2032(\u03b9)\u03b1\u2032+r(\u03b9)u\u03b2(\u03bd(\u03b9))=0,\u03b9\u2265\u03b90 where w(\u03b9)=u(\u03b9)+q(\u03b9)u(\u03b6(\u03b9)). Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.<\/jats:p>","DOI":"10.3390\/sym13030367","type":"journal-article","created":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T06:47:20Z","timestamp":1614322040000},"page":"367","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["New Theorems for Oscillations to Differential Equations with Mixed Delays"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9740-3081","authenticated-orcid":false,"given":"Shyam Sundar","family":"Santra","sequence":"first","affiliation":[{"name":"Department of Mathematics, JIS College of Engineering, Kalyani 741235, India"}]},{"given":"Debasish","family":"Majumder","sequence":"additional","affiliation":[{"name":"Department of Mathematics, JIS College of Engineering, Kalyani 741235, India"}]},{"given":"Rupak","family":"Bhattacharjee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, JIS College of Engineering, Kalyani 741235, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-9608","authenticated-orcid":false,"given":"Omar","family":"Bazighifan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4167-1690","authenticated-orcid":false,"given":"Khaled Mohamed","family":"Khedher","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia"},{"name":"Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1552-3763","authenticated-orcid":false,"given":"Marin","family":"Marin","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computers Science, Transilvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Berezansky, L., Domoshnitsky, A., and Koplatadze, R. 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