Existence and Structure of Extremals for One-Dimensional Nonautonomous Variational Problems

A. J. Zaslavski
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A. J. Zaslavski: Technion-Israel Institute of Technology

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 3, No 10, 757 pages

Abstract: Abstract We study the existence and structure of extremals for one-dimensional variational problems on a torus and the properties of the minimal average action as a function of the rotation number. We show that, for a generic integrand f, the minimum of the minimal average action is attained at a rational point mn −1 where n≥1 and m are integers; also, for each initial value, there exists an (f)-weakly optimal solution over an infinite horizon.

Keywords: Infinite horizons; weakly optimal solutions; turnpike property; minimal average action; rotation number (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022602512064

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