Lyapunov inequality for linear Hamiltonian systems on time scales

The principal aim of this paper is to state and prove some Lyapunov inequalities for linear Hamiltonian system on an arbitrary time scale T, so that the well-known case of differential linear Hamiltonian systems (T=R) and the recently developed case of discrete Hamiltonian systems (T=Z) are unified. Applying these inequalities, a disconjugacy criterion for Hamiltonian systems on time scales is obtained.