Kari Fowler

Publication Date

2004

Document Type

Dissertation/Thesis

First Advisor

Sons, Linda R.

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

LCSH

Differential equations

Abstract

In this research work we consider complex differential equations in the unit disk and study relationships between the coefficients of such equations and their solutions. Our concern in this study is with global solutions for the differential equations, i.e., ones which are defined and satisfy the differential equation throughout the unit disk. In particular, we study the influence of the normality of the coefficients on the solutions of linear homogeneous differential equations and also the influence of the normality of a solution on the coefficients. We further study the interaction between the coefficients and solutions of both homogeneous and Riccati differential equations in terms of the MacLane class. Later in the dissertation, we explore meromorphic and Riccati versions of a Fundamental Lemma of MacLane. Finally, we give conditions under which a differential polynomial assumes all complex values infinitely often.

Comments

Includes bibliographical references (pages [74]-76).

Extent

76 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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