Date of Award:
5-1992
Document Type:
Dissertation
Degree Name:
Doctor of Philosophy (PhD)
Department:
Mathematics and Statistics
Committee Chair(s)
Jerry R. Ridenhour
Committee
Jerry R. Ridenhour
Committee
Robert Gunderson
Committee
Lance Littlejohn
Committee
Duane Loveland
Committee
Russell Thompson
Abstract
This dissertation is both a literature survey and a presentation of new and independent results.
The survey gives an overview of disconjugacy and oscillation theory for linear differential and difference equations with an emphasis on comparing the theory of difference equations to the theory of differential equations. Second order scalar equations, higher order scalar equations, matrix equations (systems) and Hamiltonian systems are discussed. A chapter on three-term recurrences of systems is also included. Both similarities and differences between differential and difference equations are described.
The new and independent results are for Hamiltonian systems of difference equations. Those results include the representation of any solution in terms of an isotropic solution, necessary conditions for disconjugacy, the development of appropriate Riccati equations and the existence of principal solutions.
Checksum
325a679fcc2f34c7ec60623bbaa87178
Recommended Citation
Xu, Yuhua, "Disconjugacy and Oscillation Theory of Linear Differential and Difference Equations" (1992). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7130.
https://digitalcommons.usu.edu/etd/7130
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