Fixed-Period Problems: The Sublinear Case

  • Ivar Ekeland
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 19)


With this chapter, the preliminaries are over, and we begin the search for periodic solutions to Hamiltonian systems. All this will be done in the convex case; that is, we shall study the boundary-value problem
$$ \left\{ {\begin{array}{*{20}c} {\dot x = JH'\left( {t,x} \right)} \\ {x\left( 0 \right) = x\left( T \right)} \\ \end{array} } \right. $$
with H (t, ·) a convex function of x, going to +∞ when ∥ x ∥ → ∞.


Periodic Solution Hamiltonian System Autonomous System Minimal Period Dual Action 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Ivar Ekeland
    • 1
  1. 1.CEREMADEUniversité Paris-DauphineParis Cedex 16France

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