Eigenwertprobleme und Oszillation linearer Hamiltonscher Systeme
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
LicenseStandard (Fassung vom 03.05.2003)
The present dissertation deals with the oscillation behavior of linear Hamiltonian systems and related eigenvalue problems with general, linear independent self-adjoint boundary conditions. The main new aspect of this dissertation is the fact that we do not require controllability, strong observability or strong normality of the system. In view of this generalization it is necessary to introduce a new notion of "proper" eigenvalues and their multiplicities of the related eigenvalue problem. We show that the "proper" eigenvalues of the related eigenvalue problems are always isolated. Furthermore we introduce a new notion of the multiplicity of a "proper" focal point of so-called conjoined bases of the differential system. We derive oscillation theorems which give a formula for the number of all "proper" eigenvalues (including multiplicities) smaller or equal than a certain constant with respect to the number of all "proper" focal points (including multiplicities) of a certain conjoined basis of the Hamiltonian system. Due to our generalization we are able to treat more general Sturm-Liouville eigenvalue problems as in the existing literature.
Subject HeadingsEigenwertproblem [GND]
Hamiltonsches System [GND]
Hamiltonian systems [LCSH]