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Optimization Letters

, Volume 5, Issue 4, pp 587–599 | Cite as

A general backwards calculus of variations via duality

  • Agnieszka B. Malinowska
  • Delfim F. M. TorresEmail author
Original Paper

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.

Keywords

Calculus of variations Composition of functionals Euler–Lagrange equations Natural boundary conditions Time scales Duality 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Agnieszka B. Malinowska
    • 1
  • Delfim F. M. Torres
    • 2
    Email author
  1. 1.Faculty of Computer ScienceBiałystok University of TechnologyBiałystokPoland
  2. 2.Department of MathematicsUniversity of AveiroAveiroPortugal

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