{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:29:09Z","timestamp":1760239749657,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,27]],"date-time":"2020-12-27T00:00:00Z","timestamp":1609027200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007801","name":"Fundaci\u00f3n S\u00e9neca","doi-asserted-by":"publisher","award":["20783\/PI\/18"],"award-info":[{"award-number":["20783\/PI\/18"]}],"id":[{"id":"10.13039\/100007801","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-097198-B-I00"],"award-info":[{"award-number":["PGC2018-097198-B-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of the present work is to study the necessary and sufficient conditions for the existence of periodic solutions for a class of third order differential equations by using the averaging theory. 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