{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T11:47:38Z","timestamp":1748000858965,"version":"3.40.5"},"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":[{"name":"King Mongkut\u2019s University of Technology North Bangkok, Thailand"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We study a new class of three-point boundary value problems of nonlinear second-order<jats:italic>q<\/jats:italic>-difference equations. Our problems contain different numbers of<jats:italic>q<\/jats:italic>in derivatives and integrals. By using a variety of fixed point theorems (such as Banach\u2019s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii\u2019s fixed point theorem, and Leray-Schauder nonlinear alternative) and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. Illustrative examples are also presented.<\/jats:p>","DOI":"10.1155\/2013\/763786","type":"journal-article","created":{"date-parts":[[2013,10,24]],"date-time":"2013-10-24T06:23:36Z","timestamp":1382595816000},"page":"1-12","source":"Crossref","is-referenced-by-count":8,"title":["Three-Point Boundary Value Problems of Nonlinear Second-Order<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:math>-Difference Equations Involving Different Numbers of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:math>"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":true,"given":"Thanin","family":"Sitthiwirattham","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8185-3539","authenticated-orcid":true,"given":"Jessada","family":"Tariboon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok, Thailand"}]},{"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.2307\/2370183"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.2307\/2369887"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.2307\/2370216"},{"key":"4","first-page":"195","volume":"30","year":"1929","journal-title":"American Mathematics II"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02547785"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00739095"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1063\/1.531800"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(93)90289-C"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00761122"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(95)00253-7"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02100180"},{"year":"1990","key":"13"},{"key":"14","first-page":"63","volume":"23","year":"1999","journal-title":"Annales des Sciences Math\u00e9matiques du Qu\u00e9bec"},{"year":"2002","key":"15"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2003.09.004"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.06.009"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s11139-006-0259-8"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2009.02.044"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.09.061"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-09-10185-5"},{"key":"22","first-page":"1","volume":"94","year":"2011","journal-title":"Electronic Journal of Differential Equations"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2012-35"},{"key":"24","first-page":"59","volume":"19","year":"2012","journal-title":"Communications on Applied Nonlinear Analysis"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2012-81"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/292860"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2013-113"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2013-124"},{"key":"29","doi-asserted-by":"publisher","DOI":"10. 1155\/2013\/605169"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1969-0239559-9"},{"key":"31","first-page":"123","volume":"10","year":"1955","journal-title":"Uspekhi Matematicheskikh Nauk"},{"year":"2003","key":"32"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/763786.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/763786.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/763786.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T20:07:32Z","timestamp":1471550852000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/763786\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":31,"alternative-id":["763786","763786"],"URL":"https:\/\/doi.org\/10.1155\/2013\/763786","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}