{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T09:59:05Z","timestamp":1755597545878},"reference-count":20,"publisher":"Hindawi Limited","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\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Abstract and Applied Analysis"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given.<\/jats:p>","DOI":"10.1155\/2014\/631281","type":"journal-article","created":{"date-parts":[[2014,4,7]],"date-time":"2014-04-07T23:10:09Z","timestamp":1396912209000},"page":"1-7","source":"Crossref","is-referenced-by-count":2,"title":["Necessary Condition for an Euler-Lagrange Equation on Time Scales"],"prefix":"10.1155","volume":"2014","author":[{"given":"Monika","family":"Dryl","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/BF03323153"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0201-1"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00432-0"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8230-9"},{"issue":"2","key":"5","first-page":"399","volume":"42","year":"2013","journal-title":"Control and Cybernetics Journal"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1137\/130912219"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.3934\/naco.2013.3.145"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1177\/1077546309103268"},{"issue":"1","key":"9","first-page":"27","volume":"8","year":"2013","journal-title":"International Journal of Difference Equations"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.11.035"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2012.754435"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.2307\/1989443"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.03.003"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1051\/ijsmdo\/2010003"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2010.08.023"},{"key":"17","series-title":"Universitext","year":"2004"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2010.05.001"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.06.022"},{"key":"20","year":"2014"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.12.006"}],"container-title":["Abstract and Applied Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2014\/631281.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2014\/631281.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2014\/631281.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T03:41:40Z","timestamp":1469763700000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aaa\/2014\/631281\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":20,"alternative-id":["631281","631281"],"URL":"https:\/\/doi.org\/10.1155\/2014\/631281","relation":{},"ISSN":["1085-3375","1687-0409"],"issn-type":[{"value":"1085-3375","type":"print"},{"value":"1687-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}