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The turnpike result for approximate solutions of nonautonomous variational problems

Part of: Existence theories Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

Alexander J. Zaslavski
Alexander J. Zaslavski
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel, e-mail: ajzasl@techunix.technion.ac.il
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Abstract

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In this work we study the structure of approximate solutions of variational problems with continuous integrands f: [0, ∞) × Rn × Rn → R1 which belong to a complete metric space of functions. The main result in this paper deals with the turnpike property of variational problems. To have this property means that the approximate solutions of the problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions, except in regions close to the endpoints.

Keywords

Complete metric spacegood functionintegrandturnpike property.

MSC classification

Secondary: 49J99: None of the above, but in this section 54E52: Baire category, Baire spaces

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 1 , February 2006 , pp. 105 - 130
Copyright
Copyright © Australian Mathematical Society 2006

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