Title: Bounded solutions for a class of Hamiltonian systems,
Abstract: We obtain bounded for all $t$ solutions of ordinary differential equations as
limits of the solutions of the corresponding Dirichlet problems on $(-L,L)$,
with $L \rightarrow \infty$. We derive a priori estimates for the Dirichlet
problems, allowing passage to the limit, via a diagonal sequence. This approach
carries over to the PDE case.