Research Seminar in Analysis

in conjunction with the Colloquium at UMR

meets again in G5 (Rolla Building)

on Friday, November 8, 2002, 3:30 pm.

All interested faculty and students are invited to attend.

Werner Kratz (Universität Ulm) is lecturing on
Continuous and Discrete Oscillation.

In the first part of this talk we give an overview and old and recent results concerning the oscillation properties of so-called Hamiltonian differential systems, which include e.g. higher order Sturm-Liouville differential equations. In the second part we discuss the corresponding results for discrete equations, more precisely, for symplectic difference systems, which include Hamiltonian difference systems and also Sturm-Liouville difference equations. Moreover, we compare the results and their proofs for the continuous and discrete equations. Finally, in the third part we present a new result on the nonoscillation of the continuous (i.e., differential) equations without assuming controllability (or normality). This requires a generalization of the notion of focal points ("zeros").