In this paper we establish the Rayleigh principle, i.e., the variational characterization of the eigenvalues, for a general eigenvalue problem consisting of a time scale symplectic system and the Dirichlet boundary conditions. No normality or controllability assumption is imposed on the system. Applications of this result include the Sturmian comparison and separation theorems for time scale symplectic systems. This paper generalizes and unifies the corresponding results obtained recently for the discrete symplectic systems and continuous time linear Hamiltonian systems. The results are also new and particularly interesting for the case when the considered time scale is ``special'', that is, consisting of a union of finitely many disjoint compact real intervals and/or finitely many isolated points.

Last change: October 24, 2011. (c) Roman Simon Hilscher