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Abstract and Applied Analysis
Volume 2014, Article ID 631281, 7 pages
Research Article

Necessary Condition for an Euler-Lagrange Equation on Time Scales

Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Received 28 January 2014; Accepted 13 March 2014; Published 7 April 2014

Academic Editor: Ryan Loxton

Copyright © 2014 Monika Dryl and Delfim F. M. Torres. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.