A General Delta-Nabla Calculus of Variations on Time Scales with Application to Economics

We consider a general problem of the calculus of variations on time scales with a cost functional that is the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange delta-nabla differential equations are proved, which lead to important insights in the process of discretization. Application of the obtained results to a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness is discussed.