Convexity Methods in Hamiltonian Mechanics pp 110-135 | Cite as
Fixed-Period Problems: The Sublinear Case
Chapter
Abstract
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 with H (t, ·) a convex function of x, going to +∞ when ∥ x ∥ → ∞.
$$
\left\{ {\begin{array}{*{20}c}
{\dot x = JH'\left( {t,x} \right)} \\
{x\left( 0 \right) = x\left( T \right)} \\
\end{array} } \right.
$$
(1)
Keywords
Periodic Solution Hamiltonian System Autonomous System Minimal Period Dual Action
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© Springer-Verlag Berlin Heidelberg 1990