Title: A general delta-nabla calculus of variations on time scales with application to economics

Authors: Monika Dryl; Delfim F.M. Torres

Addresses: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal ' Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

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 discretisation. 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 maximise its future market competitiveness is discussed.

Keywords: time scales; calculus of variations; Euler-Lagrange equations; discretisation; economics; cost function; delta integrals; nabla integrals; differential equations; production rate; investment policy.

DOI: 10.1504/IJDSDE.2014.067108

International Journal of Dynamical Systems and Differential Equations, 2014 Vol.5 No.1, pp.42 - 71

Available online: 23 Jan 2015 *

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