Isoperimetric problems on time scales with nabla derivatives

Abstract

We prove a necessary optimality condition for isoperimetric problems under nabla-differentiable curves. As a consequence, the recent results of [M.R. Caputo, A unified view of ostensibly disparate isoperimetric variational problems, Appl. Math. Lett. (2008), doi:10.1016/j.aml.2008.04.004], that put together seemingly dissimilar optimal control problems in economics and physics, are extended to a generic time scale. We end with an illustrative example of application of our main result to a dynamic optimization problem from economics.

This is a preprint of an article whose final and definitive form will be published in the Journal of Vibration and Control. Date Accepted: November 21, 2008

References in corpus (3)

• Calculus of Variations on Time Scales with Nabla Derivatives
• Higher-Order Calculus of Variations on Time Scales
• Necessary and sufficient conditions for local Pareto optimality on time scales

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