All ETDs from UAB

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.

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