Properties of the Solutions of Complex Differential and Difference Equations

Abstract

This thesis investigates meromorphic solutions of linear differential and differentialdifference equations in the complex plane using Nevanlinna theory. We study the growth, order, and fixed points of solutions to equations whose coefficients are entire or meromorphic functions of [p,q]-order. In particular, for differential-difference equations, we analyze the growth and the zero distribution of meromorphic solutions. For differential equations, we extend previous results from the unit disc to the entire complex plane and provide generalizations for both homogeneous and nonhomogeneous equations, offering a unified framework for understanding the behavior and oscillation of meromorphic solutions.