A general backwards calculus of variations via duality - Malinowska, A.B.
We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals. © 2010 Springer-Verlag.