{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T10:48:50Z","timestamp":1774262930357,"version":"3.50.1"},"reference-count":18,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We are concerned with the following third-order three-point boundary value problem:<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>u<\/mml:mi><mml:mi>\u2034<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>t<\/mml:mi><mml:mo>)=<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>t<\/mml:mi><mml:mi>,u<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>t<\/mml:mi><mml:mo>)),<\/mml:mo><mml:mi mathvariant=\"normal\"\/><mml:mi mathvariant=\"normal\">t<\/mml:mi><mml:mo>\u2208[<\/mml:mo><mml:mn mathvariant=\"normal\">0,1<\/mml:mn><mml:mo>],<\/mml:mo><mml:mi>u<\/mml:mi><mml:mi>\u2032<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">0<\/mml:mn><mml:mo>)=<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo>)=<\/mml:mo><mml:mn mathvariant=\"normal\">0,<\/mml:mn><mml:mi mathvariant=\"normal\"\/><mml:mi mathvariant=\"normal\">u<\/mml:mi><mml:mi>\u2033<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\u03b7<\/mml:mi><mml:mo>)+<\/mml:mo><mml:mi>\u03b1u<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">0<\/mml:mn><mml:mo>)=<\/mml:mo><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>\u03b1<\/mml:mi><mml:mo>\u2208[<\/mml:mo><mml:mn mathvariant=\"normal\">0,2<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\u03b7<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mrow><mml:mo stretchy=\"false\">[<\/mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><mml:mo>\/<\/mml:mo><mml:mrow><mml:mn mathvariant=\"normal\">3,<\/mml:mn><\/mml:mrow><\/mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>. Although corresponding Green's function is sign-changing, we still obtain the existence of monotone positive solution under some suitable conditions on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><\/mml:math>by applying iterative method. An example is also included to illustrate the main results obtained.<\/jats:p>","DOI":"10.1155\/2014\/541234","type":"journal-article","created":{"date-parts":[[2014,3,20]],"date-time":"2014-03-20T03:02:21Z","timestamp":1395284541000},"page":"1-6","source":"Crossref","is-referenced-by-count":6,"title":["Iteration for a Third-Order Three-Point BVP with Sign-Changing Green's Function"],"prefix":"10.1155","volume":"2014","author":[{"given":"Ya-Hong","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing-Long","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"3","volume":"22","year":"1987"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(03)00132-X"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.7153\/mia-09-42"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2007.03.008"},{"issue":"155","key":"13","first-page":"1","volume":"2010","year":"2010","journal-title":"Electronic Journal of Differential Equations"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.10.029"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-003-0087-1"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2007.01.045"},{"key":"4","volume":"5","year":"1988"},{"key":"9","year":"1964"},{"issue":"2","key":"14","first-page":"219","volume":"16","year":"2012","journal-title":"Communications in Applied Analysis"},{"issue":"118","key":"15","first-page":"1","volume":"2012","year":"2012","journal-title":"Electronic Journal of Differential Equations"},{"issue":"215","key":"16","first-page":"1","volume":"2013","year":"2013","journal-title":"Electronic Journal of Differential Equations"},{"issue":"30","key":"10","first-page":"1","volume":"2013","year":"2013","journal-title":"Electronic Journal of Qualitative Theory of Differential Equations"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(02)00125-7"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1216\/jiea\/1181074944"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-005-0039-y"},{"key":"11","year":"1976"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/541234.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/541234.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/541234.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T01:57:41Z","timestamp":1469757461000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/541234\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":18,"alternative-id":["541234","541234"],"URL":"https:\/\/doi.org\/10.1155\/2014\/541234","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}