{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:47:15Z","timestamp":1760233635021,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,6]],"date-time":"2021-02-06T00:00:00Z","timestamp":1612569600000},"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>In this work, we present several oscillation criteria for higher-order nonlinear delay differential equation with middle term. Our approach is based on the use of Riccati substitution, the integral averaging technique and the comparison technique. The symmetry contributes to deciding the right way to study oscillation of solutions of this equations. Our results unify and improve some known results for differential equations with middle term. Some illustrative examples are provided.<\/jats:p>","DOI":"10.3390\/sym13020278","type":"journal-article","created":{"date-parts":[[2021,2,7]],"date-time":"2021-02-07T14:07:19Z","timestamp":1612706839000},"page":"278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["More Effective Conditions for Oscillatory Properties of Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"given":"Taher A.","family":"Nofal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}]},{"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\/0000-0003-0738-787X","authenticated-orcid":false,"given":"Mihai","family":"Postolache","sequence":"additional","affiliation":[{"name":"Center for General Education, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Interior Design, Asia University, Taichung 41354, Taiwan"},{"name":"Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania"},{"name":"Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hale, J.K. 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