A General Delta-Nabla Calculus of Variations on Time Scales with Application to Economics
arXiv:1410.1190 · doi:10.1504/IJDSDE.2014.067108
Abstract
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.
This is a preprint of a paper whose final and definite form will be published in the Int. J. Dyn. Syst. Differ. Equ. (IJDSDE), ISSN 1752-3583. Paper submitted 17/Jul/2014; revised 21/Sept/2014 and 03/Oct/2014; accepted for publication 05/Oct/2014