A General Backwards Calculus of Variations via Duality
Agnieszka B. Malinowska, Delfim F. M. Torres
TL;DR
This paper develops a unified backward calculus of variations framework on arbitrary time scales, deriving necessary optimality conditions for complex nabla integral problems and their combinations.
Contribution
It introduces a general duality-based approach to derive Euler-Lagrange and boundary conditions for nabla variational problems on arbitrary time scales.
Findings
Derived Euler-Lagrange equations for nabla integrals
Established natural boundary conditions for these problems
Extended results to product and quotient of nabla functionals
Abstract
We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.
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