Date of Award:

5-1992

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Advisor/Chair:

Jerry R. Ridenhour

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. 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.

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22bb864c9fb68fe96afbdf6a24c26aea

Included in

Mathematics Commons

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