Euler-Lagrange equations for composition functionals in calculus of variations on time scales

Abstract

In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function H with the delta integral of a vector valued field f, i.e., of the form H (int;ba f(t,xσ(t); δ(t))δt). Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.