Backward variational approach on time scales with an action depending on   the free endpoints
  We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales via the backward nabla differential operator. 
Agnieszka B. Malinowska, Delfim F. M. Torres
math.OC math-ph math.MP