{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:35:14Z","timestamp":1753886114057,"version":"3.41.2"},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,12,31]],"date-time":"2009-12-31T00:00:00Z","timestamp":1262217600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Differential Equations"],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>The oscillatory behavior of the solutions of the\nsecond\u2010order linear nonautonomous equation <jats:italic>x<\/jats:italic>(<jats:italic>n<\/jats:italic> + 1) = <jats:italic>a<\/jats:italic>(<jats:italic>n<\/jats:italic>)<jats:italic>x<\/jats:italic>(<jats:italic>n<\/jats:italic>) \u2212 <jats:italic>b<\/jats:italic>(<jats:italic>n<\/jats:italic>)<jats:italic>x<\/jats:italic>(<jats:italic>n<\/jats:italic> \u2212 1), <jats:italic>\u2009\u2009<\/jats:italic><jats:italic>n<\/jats:italic> \u2208 <jats:italic>\u2115<\/jats:italic><jats:sub>0<\/jats:sub>, \nwhere <jats:italic>a<\/jats:italic>, <jats:italic>b<\/jats:italic> : <jats:italic>\u2115<\/jats:italic><jats:sub>0<\/jats:sub> \u2192 <jats:italic>\u211d<\/jats:italic>, is studied. Under the assumption that the sequence <jats:italic>b<\/jats:italic>(<jats:italic>n<\/jats:italic>)\n dominates somehow <jats:italic>a<\/jats:italic>(<jats:italic>n<\/jats:italic>), the amplitude of the oscillations and the asymptotic behavior of its solutions are also analized. \n<\/jats:p>","DOI":"10.1155\/2010\/596350","type":"journal-article","created":{"date-parts":[[2009,12,31]],"date-time":"2009-12-31T15:30:28Z","timestamp":1262273428000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Oscillatory Nonautonomous Lucas Sequences"],"prefix":"10.1155","volume":"2010","author":[{"given":"Jos\u00e9 M.","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Sandra","family":"Pinelas","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,12,31]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0507-1"},{"key":"e_1_2_6_2_2","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","volume-title":"Difference Equations and Inequalities","author":"Agarwal R. 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Oscillatory difference equations and moment problems to appear inInternational Journal of Difference Equations."}],"container-title":["International Journal of Differential Equations"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijde\/2010\/596350.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijde\/2010\/596350.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2010\/596350","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T14:10:38Z","timestamp":1718633438000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2010\/596350"}},"subtitle":[],"editor":[{"given":"Elena","family":"Braverman","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2009,12,31]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1155\/2010\/596350"],"URL":"https:\/\/doi.org\/10.1155\/2010\/596350","archive":["Portico"],"relation":{},"ISSN":["1687-9643","1687-9651"],"issn-type":[{"type":"print","value":"1687-9643"},{"type":"electronic","value":"1687-9651"}],"subject":[],"published":{"date-parts":[[2009,12,31]]},"assertion":[{"value":"2009-09-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-12-03","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-12-31","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"596350"}}