Necessary condition for an Euler-Lagrange equation on time scales
  We prove a necessary condition for a dynamic integro-differential 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. 
Monika Dryl, Delfim F. M. Torres
math.OC