caa a22 4500 39753275X CHVBK 20180308164656.0 cr unu---uuuuu 161202e199504 xx s 000 0 eng 10.1112/jlms/51.2.401 doi (NATIONALLICENCE)oxford-10.1112/jlms/51.2.401 Kratz Werner Abteilung Mathematik V, Universität Ulm Helmholtzstrasse 18, D-89069 Ulm, Germany An Oscillation Theorem for Self-Adjoint Differential Systems and the Rayleigh Principle for Quadratic Functionals [Elektronische Daten] [Werner Kratz] In this note an oscillation theorem on self-adjoint differential systems of the form ẋ = Ax + Bu, u̇ = (C − λ 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. © The London Mathematical Society Notes and Papers nationallicence Journal of the London Mathematical Society Oxford University Press 51/2(1995-04), 401-416 0024-6107 51:2<401 1995 51 jlms https://doi.org/10.1112/jlms/51.2.401 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1112/jlms/51.2.401 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kratz Werner Abteilung Mathematik V, Universität Ulm Helmholtzstrasse 18, D-89069 Ulm, Germany NATIONALLICENCE 773 0- Journal of the London Mathematical Society Oxford University Press 51/2(1995-04), 401-416 0024-6107 51:2<401 1995 51 jlms Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford