A General Backwards Calculus of Variations via Duality
arXiv:1007.1679 · doi:10.1007/s11590-010-0222-x
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.
Submitted to Optimization Letters 03-June-2010; revised 01-July-2010; accepted for publication 08-July-2010
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Cited by in corpus (12)
- Generalized transversality conditions for the Hahn quantum variational calculus
- Generalizing the variational theory on time scales to include the delta indefinite integral
- Optimality conditions for the calculus of variations with higher-order delta derivatives
- Composition Functionals in Fractional Calculus of Variations
- Existence of solutions for dynamic inclusions on time scales via duality
- The Variational Calculus on Time Scales
- Direct and Inverse Variational Problems on Time Scales: A Survey
- Necessary optimality conditions for infinite horizon variational problems on time scales
- Fractional Calculus of Variations for Double Integrals
- Non shifted calculus of variations on time scales with Nabla-differentiable Sigma
- L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
- The second Noether theorem on time scale