Sons, Linda R.
Ph.D. (Doctor of Philosophy)
Department of Mathematical Sciences
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.
Fowler, Kari, "Normal functions, the MacLane class, and complex differential equations in the unit disk" (2004). Graduate Research Theses & Dissertations. 4135.
Northern Illinois University
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