Isoperimetric problems on time scales with nabla derivatives

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Almeida, Ricardo
Torres, Delfim F. M.
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Abstract
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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.
Comment: 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
Keywords
Mathematics - Optimization and Control, 49K30, 39A12
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