Physical Sciences and Mathematics Commons^™

Disconjugacy And Oscillation Theory Of Linear Differential And Difference Equations, Yuhua Xu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

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 …