Israel Journal of Mathematics

, Volume 67, Issue 3, pp 337–344 | Cite as

Calculus of variations in mean and convex lagrangians, III

  • Joël Blot


For the almost periodic or periodic solution of an Euler-Lagrange equation, with a convex lagrangian, under a condition of symmetry on the lagrangian, we establish a necessary condition that involves the second differential of the lagrangian. We deduce from this some results of non-existence.


Periodic Solution Fourier Series Convex Function Convex Subset Orthogonal Projector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. S. Besicovitch,Almost Periodic Functions, Cambridge Univ. Press, Cambridge, 1932.Google Scholar
  2. 2.
    J. Blot,Une approache variationnelle des orbites quasi-périodiques des Systèmes Hamiltoniens, Ann. Sci. Math. Québec, to appear.Google Scholar
  3. 3.
    J. Blot,Calculus of variations in mean and convex Lagrangians, J. Math. Anal. Appl.134 (1988), 312–321.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    J. Blot,Calcul des variations en moyenne temporelle, Note C. R. Acad. Sci. Paris306, Série I (1988), 809–811.MATHMathSciNetGoogle Scholar
  5. 5.
    J. Blot,Calculus of variations in mean and convex lagrangians, II, Bull. Aust. Math. Soc., to appear.Google Scholar
  6. 6.
    F. H. Clarke,Optimization and Nonsmooth Analysis, Wiley, New York, 1983.MATHGoogle Scholar
  7. 7.
    I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai,Ergodic Theory, Springer-Verlag, New York, 1982.MATHGoogle Scholar
  8. 8.
    R. E. Gaines and J. K. Peterson,Periodic solutions to differential inclusions, Nonlinear Anal.5 (1981), 1109–1131.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    R. T. Rockafellar,Generalized hamiltonian equations for convex problems of Lagrange, Pacific J. Math.33 (1970), 411–427.MATHMathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press of Israel 1989

Authors and Affiliations

  • Joël Blot
    • 1
  1. 1.Faculté des Sciences de LimogesUniversité de Limoges, Département de MathématiquesLimoges CédexFrance

Personalised recommendations