{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T12:07:53Z","timestamp":1648814873131},"reference-count":29,"publisher":"Hindawi Limited","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":"Scientific Research Fund of Sichuan Provincial Education Department of China"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>This paper deals with a generalized form of nonlinear retarded Gronwall-Bellman type integral inequality in which the maximum of the unknown function of two variables is involved. This form includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals. Requiring neither monotonicity nor separability of given functions, we apply a technique of monotonization to estimate the unknown function. Our result can be used to weaken conditions for some known results. We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.<\/jats:p>","DOI":"10.1155\/2013\/853476","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T17:02:08Z","timestamp":1363798928000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables"],"prefix":"10.1155","volume":"2013","author":[{"given":"Yong","family":"Yan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sichuan University for Nationalities, Kangding, Sichuan 626001, China"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.2307\/1967124"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-43-01059-2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02022967"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7085"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.04.067"},{"issue":"3","key":"6","first-page":"387","volume":"33","year":"1990","journal-title":"Funkcialaj Ekvacioj"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.02.099"},{"key":"8","year":"1992"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2001.7743"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.06.009"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1155\/JIA.2005.347"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(03)00409-8"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7134"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1995.1008"},{"key":"15","year":"1998"},{"key":"16","series-title":"North-Holland Mathematics Studies","volume":"205","year":"2006"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(01)00070-X"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/409809"},{"key":"19","first-page":"409","volume":"3","year":"1957","journal-title":"Advances in Mathematics (China)"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1080\/00036818308839468"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.09.030"},{"key":"22","year":"1966"},{"key":"23","year":"2011"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1080\/00036819808840689"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1216\/rmjm\/1187453110"},{"issue":"4","key":"26","first-page":"811","volume":"15","year":"2012","journal-title":"Mathematical Inequalities and Applications"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.10.024"},{"issue":"4","key":"28","first-page":"523","volume":"4","year":"2010","journal-title":"Journal of Mathematical Inequalities"},{"issue":"1","key":"29","first-page":"57","volume":"6","year":"2011","journal-title":"Advances in Dynamical Systems and Applications"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/853476.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/853476.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/853476.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T15:07:08Z","timestamp":1469891228000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/853476\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":29,"alternative-id":["853476","853476"],"URL":"https:\/\/doi.org\/10.1155\/2013\/853476","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}