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Lyapunov inequalities for time scales. (English) Zbl 1088.34503
Summary: The theory of time scales has been introduced in order to unify discrete and continuous analysis. We present a Lyapunov inequality for Sturm-Liouville dynamical equations of second order on such time scales, which can be applied to obtain a disconjugacy criterion for these equations. We also extend the presented material to the case of a general linear Hamiltonian dynamical system on time scales. Some special cases of our results contain the classical Lyapunov inequalities for differential equations as well as only recently developed Lyapunov inequalities for difference equations.
MSC:
34A40Differential inequalities (ODE)
39A10Additive difference equations
39A13Difference equations, scaling (q-differences)
26D15Inequalities for sums, series and integrals of real functions