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(∫abf(t,xσ(t),x(t)) t). 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.
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