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. higher order scalar equations. Second 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.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8238 |
| Date | 01 May 1992 |
| Creators | Xu, Yuhua |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact digitalcommons@usu.edu. |
Page generated in 0.0016 seconds