STUDY OF THE PROPERTIES OF GROWTH AND OSCILLATION OF SOLUTIONS FOR CERTAIN TYPES OF COMPLEX DIFFERENTIAL EQUATIONS

Abstract

The determination of the order of entire and meromorphic functions plays an important role in Nevanlinna’s value distribution theory. Several extensions on the original definition of the order have been made to characterise the asymptotic behaviour of fast growing functions. In this thesis, we use a generalized concept of order, called the ϕ-order, to investigate the properties of growth and oscillation of solutions for homogeneous and nonhomogeneous higher order complex linear differential equations. We describe in terms of growth of order and exponent of convergence the relationship between the solutions of differential equations and their coefficients in the complex plane as well as in the unit disc. We provide various generalizations and improvements of many previous works on this subject.