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Calculus of variations in mean and convex Lagrangians, II

Published online by Cambridge University Press:  17 April 2009

Joël Blot
Joël Blot
Affiliation:
Faculté des Sciences de LimogesDépartment de Mathématiques123 Av. Albert Thomas87060 Limoges CedexFrance
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Abstract

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We prove the Legendre Necessary Condition of the Calculus of Variations in Mean an arbitrary finite dimension. When the Lagrangian is convex, we establish that if the Euler-Lagrange equation possesses an almost periodic solution then it possesses periodic and constant solutions. We deduce from this fact various consequences on the structure of the set of almost periodic solutions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 457 - 463
Copyright
Copyright © Australian Mathematical Society 1989

References

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