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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Coupled points in the calculus of variations and applications to periodic problems


Authors: Vera Zeidan and Pier Luigi Zezza
Journal: Trans. Amer. Math. Soc. 315 (1989), 323-335
MSC: Primary 49B21; Secondary 49D50
DOI: https://doi.org/10.1090/S0002-9947-1989-0961599-X
MathSciNet review: 961599
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Abstract: The aim of this paper is to introduce the definition of coupled points for the problems of the calculus of variations with general boundary conditions, and to develop second order necessary conditions for optimality. When one of the end points is fixed, our necessary conditions reduce to the known ones involving conjugate points. We also apply our results to the periodic problems of the calculus of variations.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0961599-X
Keywords: Calculus of variations, nonlinear boundary value problems, coupled points, periodic problems
Article copyright: © Copyright 1989 American Mathematical Society