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Journal of the London Mathematical Society 1995 51(2):401-416; doi:10.1112/jlms/51.2.401
© 1995 by London Mathematical Society
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© The London Mathematical Society

An Oscillation Theorem for Self-Adjoint Differential Systems and the Rayleigh Principle for Quadratic Functionals

Werner Kratz

Abteilung Mathematik V, Universität Ulm Helmholtzstrasse 18, D-89069 Ulm, Germany

Received 18 February 1993.

In this note an oscillation theorem on self-adjoint differential systems of the form x = Ax + Bu, u = (C – {lambda} C0)x – ATu is obtained, complementing, in particular, results of M. Morse. The application of this oscillation result yields the Rayleigh principle for quadratic functionals, respectively, the existence theorem for corresponding self-adjoint eigenvalue problems, under the central assumptions that the pair (A, B) is controllable (or identically normal) and the triple (A, B, C0) is strongly observable.


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