Special Session 48: Differential, Difference, and Dynamic Equations
This is joint work with Werner Kratz. We consider Sturm-Liouville Equations and the corresponding quadratic functional. By using a special case of Ehrling¡¯s Lemma from functional analysis we are able to show the positivity of the functional without explicit calculations and in a more general way. This leads easily to a proof of the fact that the positivity of the quadratic functional is equivalent to a certain kind of asymptotic behavior of solutions of the Riccati matrix differential equations associated with this functional.