{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:17Z","timestamp":1740134537668,"version":"3.37.3"},"reference-count":31,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11126339"],"award-info":[{"award-number":["11126339"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the formx<\/mml:mi>(<\/mml:mo>4<\/mml:mn>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:msup>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>f<\/mml:mi>(<\/mml:mo>t<\/mml:mi>,<\/mml:mo>x<\/mml:mi>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:mrow>,<\/mml:mo>x<\/mml:mi>\u2032<\/mml:mo><\/mml:msup>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:mrow>,<\/mml:mo>x<\/mml:mi>\u2032<\/mml:mo>\u2032<\/mml:mo><\/mml:mrow><\/mml:msup>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:mrow>,<\/mml:mo>x<\/mml:mi>\u2032<\/mml:mo>\u2032<\/mml:mo>\u2032<\/mml:mo><\/mml:mrow><\/mml:msup>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:mrow><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:math>,t<\/mml:mi>\u2208<\/mml:mo>[<\/mml:mo>0<\/mml:mn>,<\/mml:mo>1<\/mml:mn><\/mml:mrow>]<\/mml:mo><\/mml:mrow><\/mml:math>,x<\/mml:mi>(<\/mml:mo>0<\/mml:mn>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>x<\/mml:mi>\u2032<\/mml:mo><\/mml:msup>(<\/mml:mo>1<\/mml:mn>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>0<\/mml:mn><\/mml:math>,x<\/mml:mi>\u2032<\/mml:mo>\u2032<\/mml:mo><\/mml:mrow><\/mml:msup>(<\/mml:mo>0<\/mml:mn>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>\u222b<\/mml:mo>0<\/mml:mn>1<\/mml:mn><\/mml:msubsup>h<\/mml:mi>(<\/mml:mo>s<\/mml:mi>,<\/mml:mo>x<\/mml:mi>(<\/mml:mo>s<\/mml:mi>)<\/mml:mo><\/mml:mrow>,<\/mml:mo>x<\/mml:mi>\u2032<\/mml:mo><\/mml:msup>(<\/mml:mo>s<\/mml:mi>)<\/mml:mo><\/mml:mrow>,<\/mml:mo>x<\/mml:mi>\u2032<\/mml:mo>\u2032<\/mml:mo><\/mml:mrow><\/mml:msup>(<\/mml:mo>s<\/mml:mi>)<\/mml:mo><\/mml:mrow><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:mstyle>d<\/mml:mtext>s<\/mml:mi><\/mml:math>,x<\/mml:mi>\u2032<\/mml:mo>\u2032<\/mml:mo>\u2032<\/mml:mo><\/mml:mrow><\/mml:msup>(<\/mml:mo>1<\/mml:mn>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>0<\/mml:mn><\/mml:math>, wheref<\/mml:mi>\u2208<\/mml:mo>C<\/mml:mi>(<\/mml:mo>[<\/mml:mo>0<\/mml:mn>,<\/mml:mo>1<\/mml:mn><\/mml:mrow>]<\/mml:mo><\/mml:mrow>\u00d7<\/mml:mo>\u211d<\/mml:mi>4<\/mml:mn><\/mml:msup><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:math>,h<\/mml:mi>\u2208<\/mml:mo>C<\/mml:mi>(<\/mml:mo>[<\/mml:mo>0<\/mml:mn>,<\/mml:mo>1<\/mml:mn><\/mml:mrow>]<\/mml:mo><\/mml:mrow>\u00d7<\/mml:mo>\u211d<\/mml:mi>3<\/mml:mn><\/mml:msup><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:math>. By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.<\/jats:p>","DOI":"10.1155\/2013\/782363","type":"journal-article","created":{"date-parts":[[2013,3,24]],"date-time":"2013-03-24T17:01:01Z","timestamp":1364144461000},"page":"1-7","source":"Crossref","is-referenced-by-count":3,"title":["Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions"],"prefix":"10.1155","volume":"2013","author":[{"given":"Hui","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beihua University, Jilin City 132013, China"}]},{"given":"Libo","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beihua University, Jilin City 132013, China"}]},{"given":"Minghe","family":"Pei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beihua University, Jilin City 132013, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(84)90058-X"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2006.08.009"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.08.026"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.2307\/2048482"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.10.003"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2001.4056"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.04.013"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.07.013"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2006.03.028"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(98)00285-5"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1080\/00036818808839715"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.04.055"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00201-6"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.09.010"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(03)00131-8"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2006.11.018"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2004.06.001"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.12.027"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2004.06.001"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.06.061"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/297578"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.10.073"},{"issue":"3","key":"25","first-page":"79","volume":"9","year":"2002","journal-title":"Communications on Applied Nonlinear Analysis"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/376782"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.01.009"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210506001041"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00683-0"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(04)90037-7"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.04.002"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.02.055"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(95)00093-3"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/782363.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/782363.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/782363.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T11:13:30Z","timestamp":1469877210000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/782363\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":31,"alternative-id":["782363","782363"],"URL":"https:\/\/doi.org\/10.1155\/2013\/782363","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}