A general delta–nabla calculus of variations on time scales with application to economics. Issue 1 (1st January 2014)

• Record Type: Journal Article
• Authors: Dryl, Monika; Torres, Delfim F.M.
• Is Part Of: International journal of dynamical systems and differential equations. Volume 5:Issue 1(2015)
• Page Start: 42
• Page End: 71
• Publication Date: 2014-01-01
• Subjects: time scales -- calculus of variations -- Euler–Lagrange equations -- discretisation -- economics -- cost function -- delta integrals -- nabla integrals -- differential equations -- production rate -- investment policy; Differential equations -- Periodicals; 515.35
• DOI: 10.1504/IJDSDE.2014.067108
• Languages: English
• ISSNs: 1752-3583

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.