{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:15:08Z","timestamp":1760058908856,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T00:00:00Z","timestamp":1747008000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Researchers Supporting Project number (PNURSP2025R295), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study aims to establish new oscillation criteria for solutions of a specific class of functional differential equations. Our findings extend and refine the recently developed criteria for this type of equation by various authors and also encompass classical criteria for related problems. Our approach relies on the Riccati technique to derive conditions that preclude the possibility of non-oscillatory solutions. The inherent symmetry of these solutions plays a key role in formulating the new criteria presented here. By applying techniques from the theory of symmetric differential equations and leveraging symmetric functions, we are able to establish precise conditions for oscillation. To enhance practical applicability, we propose multiple distinct criteria while minimizing the constraints typically imposed. Several examples are provided to illustrate the accuracy, applicability, and versatility of the new criteria.<\/jats:p>","DOI":"10.3390\/sym17050740","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T03:59:26Z","timestamp":1747108766000},"page":"740","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["General Neutral Functional Differential Equations of Third Order: Enhanced Oscillation Criteria"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6959-372X","authenticated-orcid":false,"given":"A.","family":"Al Themairi","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, 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"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1977). 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