{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:07Z","timestamp":1740134527070,"version":"3.37.3"},"reference-count":18,"publisher":"Wiley","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\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11361054","11201378","2012 6203110004","1208RJZA258"],"award-info":[{"award-number":["11361054","11201378","2012 6203110004","1208RJZA258"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11361054","11201378","2012 6203110004","1208RJZA258"],"award-info":[{"award-number":["11361054","11201378","2012 6203110004","1208RJZA258"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Specialized Research Fund for the Doctoral Program","award":["11361054","11201378","2012 6203110004","1208RJZA258"],"award-info":[{"award-number":["11361054","11201378","2012 6203110004","1208RJZA258"]}]},{"name":"Gansu Provincial National Science Foundation of China","award":["11361054","11201378","2012 6203110004","1208RJZA258"],"award-info":[{"award-number":["11361054","11201378","2012 6203110004","1208RJZA258"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"We study the existence and nonexistence of positive solutions for the following fourth-order two-point boundary value problem subject to nonlinear boundary conditionsu<\/mml:mi><\/mml:mrow>\u2032\u2032\u2032\u2032<\/mml:mi><\/mml:mrow><\/mml:msup>(<\/mml:mo>t<\/mml:mi><\/mml:mrow>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>\u03bb<\/mml:mi>f<\/mml:mi>(<\/mml:mo>t<\/mml:mi>,<\/mml:mo>u<\/mml:mi>(<\/mml:mo>t<\/mml:mi><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:mrow>)<\/mml:mo><\/mml:mrow>,\u2009\u2009<\/mml:mo>t<\/mml:mi>\u2208<\/mml:mo>(<\/mml:mo>0,1<\/mml:mn><\/mml:mrow>)<\/mml:mo><\/mml:mrow>,<\/mml:mo>u<\/mml:mi>(<\/mml:mo>0<\/mml:mn><\/mml:mrow>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>0<\/mml:mn>,\u2009\u2009<\/mml:mo>u<\/mml:mi><\/mml:mrow>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup>(<\/mml:mo>0<\/mml:mn><\/mml:mrow>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>\u03bc<\/mml:mi>h<\/mml:mi>(<\/mml:mo>u<\/mml:mi>(<\/mml:mo>0<\/mml:mn><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:mrow>)<\/mml:mo><\/mml:mrow>,\u2009\u2009<\/mml:mo>u<\/mml:mi><\/mml:mrow>\u2032\u2032<\/mml:mi><\/mml:mrow><\/mml:msup>(<\/mml:mo>1<\/mml:mn><\/mml:mrow>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>0<\/mml:mn>,\u2009\u2009<\/mml:mo>u<\/mml:mi><\/mml:mrow>\u2032\u2032\u2032<\/mml:mi><\/mml:mrow><\/mml:msup>(<\/mml:mo>1<\/mml:mn><\/mml:mrow>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>\u03bc<\/mml:mi>g<\/mml:mi>(<\/mml:mo>u<\/mml:mi>(<\/mml:mo>1<\/mml:mn><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:math>, where\u03bb<\/mml:mi>><\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u00a0<\/mml:mi>\u03bc<\/mml:mi>\u2265<\/mml:mo>0<\/mml:mn><\/mml:math>are parameters, andf<\/mml:mi>:<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u00a0<\/mml:mi>1<\/mml:mn><\/mml:mrow><\/mml:mfenced>\u00d7<\/mml:mo>0<\/mml:mn>,<\/mml:mo>+<\/mml:mo>\u221e<\/mml:mi><\/mml:mrow><\/mml:mfenced>\u2192<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u00a0<\/mml:mi>+<\/mml:mo>\u221e<\/mml:mi><\/mml:mrow><\/mml:mfenced>,<\/mml:mo>\u00a0<\/mml:mi>h<\/mml:mi>:<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u00a0<\/mml:mi>+<\/mml:mo>\u221e<\/mml:mi><\/mml:mrow><\/mml:mfenced>\u2192<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u00a0<\/mml:mi>+<\/mml:mo>\u221e<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>, andg<\/mml:mi>:<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u00a0<\/mml:mi>+<\/mml:mo>\u221e<\/mml:mi><\/mml:mrow><\/mml:mfenced>\u2192<\/mml:mo>-<\/mml:mo>\u221e<\/mml:mi>,<\/mml:mo>0<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:math>are continuous. By using the fixed-point index theory, we prove that the problem has at least one positive solution for\u03bb<\/mml:mi>,\u2009\u2009<\/mml:mo>\u03bc<\/mml:mi><\/mml:math>sufficiently small and has no positive solution for\u03bb<\/mml:mi><\/mml:mrow><\/mml:math>large enough.<\/jats:p>","DOI":"10.1155\/2014\/972135","type":"journal-article","created":{"date-parts":[[2014,3,20]],"date-time":"2014-03-20T17:04:43Z","timestamp":1395335083000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions"],"prefix":"10.1155","volume":"2014","author":[{"given":"Ruikuan","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruyun","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1986","key":"1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(86)80006-3"},{"issue":"1","key":"3","first-page":"91","volume":"2","year":"1989","journal-title":"Differential and Integral Equations"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/00036810008840810"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1080\/00036819508840401"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.08.056"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.08.044"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2006.08.002"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2006.08.009"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2004.10.010"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.07.043"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.04.008"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.12.065"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.11.066"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.02.051"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2004.06.001"},{"key":"17","first-page":"1","volume":"78","year":"2005","journal-title":"Electronic Journal of Differential Equations"},{"year":"1988","key":"18"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/972135.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/972135.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/972135.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T07:58:01Z","timestamp":1469779081000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/972135\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":18,"alternative-id":["972135","972135"],"URL":"https:\/\/doi.org\/10.1155\/2014\/972135","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}