{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:20:24Z","timestamp":1770754824042,"version":"3.50.0"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,26]],"date-time":"2022-03-26T00:00:00Z","timestamp":1648252800000},"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>We studied the asymptotic behavior of fourth-order advanced differential equations of the form a\u03c5w\u2032\u2032\u2032\u03c5\u03b2\u2032+q\u03c5gw\u03b4\u03c5=0. New results are presented for the oscillatory behavior of these equations in the form of Philos-type and Hille\u2013Nehari oscillation criteria. Some illustrative examples are presented.<\/jats:p>","DOI":"10.3390\/sym14040686","type":"journal-article","created":{"date-parts":[[2022,3,27]],"date-time":"2022-03-27T21:31:25Z","timestamp":1648416685000},"page":"686","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Extended Approach to the Asymptotic Behavior and Symmetric Solutions of Advanced Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-9608","authenticated-orcid":false,"given":"Omar","family":"Bazighifan","sequence":"first","affiliation":[{"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\/0000-0003-2959-4212","authenticated-orcid":false,"given":"Ali Hasan","family":"Ali","sequence":"additional","affiliation":[{"name":"Doctoral School of Mathematical and Computational Sciences, University of Debrecen, H-4002 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2116-7382","authenticated-orcid":false,"given":"Fatemah","family":"Mofarreh","sequence":"additional","affiliation":[{"name":"Mathematical Science Department, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2154-9049","authenticated-orcid":false,"given":"Youssef N.","family":"Raffoul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH 45469, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,26]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Preface [Special issue on optimization and differential equations]","volume":"11","author":"Choquet","year":"2018","journal-title":"Discret. 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