{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:21:41Z","timestamp":1753888901380,"version":"3.41.2"},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,5,18]],"date-time":"2006-05-18T00:00:00Z","timestamp":1147910400000},"content-version":"vor","delay-in-days":137,"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":["10371006"],"award-info":[{"award-number":["10371006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Central University for Nationalities for Youth Teachers","award":["10371006"],"award-info":[{"award-number":["10371006"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We consider the following impulsive boundary value problem,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<jats:italic>x<\/jats:italic><jats:sup>\u2033<\/jats:sup>(<jats:italic>t<\/jats:italic>) = <jats:italic>f<\/jats:italic>(<jats:italic>t<\/jats:italic>, <jats:italic>x<\/jats:italic>, <jats:italic>x<\/jats:italic><jats:sup>\u2032<\/jats:sup>), <jats:italic>t<\/jats:italic> \u2208 <jats:italic>J<\/jats:italic>\\{<jats:italic>t<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>t<\/jats:italic><jats:sub>2<\/jats:sub>, \u2026, <jats:italic>t<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>},\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<jats:italic>\u0394<\/jats:italic><jats:italic>x<\/jats:italic>(<jats:italic>t<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>) = <jats:italic>I<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>(<jats:italic>x<\/jats:italic>(<jats:italic>t<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>), <jats:italic>x<\/jats:italic><jats:sup>\u2032<\/jats:sup>(<jats:italic>t<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>)), <jats:italic>\u0394<\/jats:italic><jats:italic>x<\/jats:italic><jats:sup>\u2032<\/jats:sup>(<jats:italic>t<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>) = <jats:italic>J<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>(<jats:italic>x<\/jats:italic>(<jats:italic>t<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>), <jats:italic>x<\/jats:italic><jats:sup>\u2032<\/jats:sup>(<jats:italic>t<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>)),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<jats:italic>i<\/jats:italic> = 1, 2, \u2026, <jats:italic>k<\/jats:italic>, <jats:italic>x<\/jats:italic>(0) = (0),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t. By using the\ncoincidence degree theory, a general theorem concerning the\nproblem is given. Moreover, we get a concrete existence result\nwhich can be applied more conveniently than recent results. Our\nresults extend some work concerning the usual <jats:italic>m<\/jats:italic>\u2010point boundary\nvalue problem at resonance without impulses.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/62512","type":"journal-article","created":{"date-parts":[[2006,6,20]],"date-time":"2006-06-20T09:35:51Z","timestamp":1150796151000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On  a class of second\u2010order impulsive boundary valueproblem at resonance"],"prefix":"10.1155","volume":"2006","author":[{"given":"Guolan","family":"Cai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zengji","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weigao","family":"Ge","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,5,18]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096\u20103003(99)00156\u20103"},{"key":"e_1_2_1_2_2","first-page":"76","article-title":"m-point boundary value problem for second order impulsive differential equation at resonance","volume":"9","author":"Cai G.","year":"2005","journal-title":"Mathematical Sciences Research Journal"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0362\u2010546X(95)00068\u20107"},{"key":"e_1_2_1_4_2","series-title":"Lecture Notes in Mathematics","volume-title":"Coincidence Degree, and Nonlinear Differential Equations","author":"Gaines R. 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