Advisory Committee Chair
Rudi Weikard
Advisory Committee Members
Tim Ferguson
Wenzhang Huang
Ioulia Karpechina
Mary Zvanut
Document Type
Dissertation
Date of Award
2022
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
In this thesis, we consider differential equations with distributional matrix coefficients giving particular care to periodic distributions. In pursuit of this, we first examine some cases in which there is no existence and uniqueness theorem for a given initial value problem, and then verify some properties of the minimal and maximal operators. We then focus on periodic systems and establish a Floquet Theory for such systems as well as extend several fundamental properties which are well known for periodic functions to periodic distributions. We also examine stability sets for differential equations with periodic distributional coefficients in one and two dimensions, and the relationship between stability sets and the spectrum of the differential equation.
Recommended Citation
Campbell, Kevin, "On the Spectral Theory for Ordinary Differential Equations with Distributional Coefficients with and Emphasis on the Periodic Case" (2022). All ETDs from UAB. 287.
https://digitalcommons.library.uab.edu/etd-collection/287