{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T20:00:25Z","timestamp":1758398425187},"reference-count":0,"publisher":"National Library of Serbia","issue":"1","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Appl Anal Discrete Math","APPL ANAL DISC MATH","APPL ANAL DISCR MATH","APPL ANAL DISCRETE M"],"published-print":{"date-parts":[[2011]]},"abstract":"<jats:p>The authors consider the nth-order differential equation ?(?(u(n?1)(x)))?=\n   f(x, u(x), ..., u(n?1)(x)), for 2?(0, 1), where ?: R? R is an increasing\n   homeomorphism such that ?(0) = 0, n?2, I:= [0,1], and f : I ?Rn ? R is a\n   L1-Carath?odory function, together with the boundary conditions gi(u, u?,\n   ..., u(n?2), u(i)(1)) = 0, i = 0, ..., n? 3, gn?2 (u, u?, ..., u(n?2),\n   u(n?2)(0), u(n?1)(0)) = 0, gn?1 (u, u?, ..., u(n?2), u(n?2)(1), u(n?1)(1))\n   = 0, where gi : (C(I))n?1?R ? R, i = 0, ..., n?3, and gn?2, gn?1 :\n   (C(I))n?1?R2 ? R are continuous functions satisfying certain monotonicity\n   assumptions. The main result establishes sufficient conditions for the\n   existence of solutions and some location sets for the solution and its\n   derivatives up to order (n?1). Moreover, it is shown how the monotone\n   properties of the nonlinearity and the boundary functions depend on n and\n   upon the relation between lower and upper solutions and their derivatives.<\/jats:p>","DOI":"10.2298\/aadm110221010g","type":"journal-article","created":{"date-parts":[[2011,2,21]],"date-time":"2011-02-21T13:40:18Z","timestamp":1298295618000},"page":"133-146","source":"Crossref","is-referenced-by-count":18,"title":["On the lower and upper solution method for higher order functional boundary value problems"],"prefix":"10.2298","volume":"5","author":[{"suffix":"R.","given":"John","family":"Graef","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, USA"}]},{"given":"Lingju","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, USA"}]},{"suffix":"M.","given":"Feliz","family":"Minh\u00f3s","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of \u00c9vora, Research Centre on Mathematics and its Applications (CIMA-UE), \u00c9vora, Portugal"}]},{"given":"Jo\u00e3o","family":"Fialho","sequence":"additional","affiliation":[{"name":"Researh Centre on Mathematics and its Applications (CIMA-UE), \u00c9vora, Portugal"}]}],"member":"1078","container-title":["Applicable Analysis and Discrete Mathematics"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T12:20:08Z","timestamp":1685103608000},"score":1,"resource":{"primary":{"URL":"https:\/\/doiserbia.nb.rs\/Article.aspx?ID=1452-86301100010G"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011]]}},"URL":"https:\/\/doi.org\/10.2298\/aadm110221010g","relation":{},"ISSN":["1452-8630","2406-100X"],"issn-type":[{"value":"1452-8630","type":"print"},{"value":"2406-100X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}