Growth of Entire solutions of Certain Classes of Non-Linear Differential Equations

Abstract

Nevanlinna theory was created to provide a quantitative measure of the value distribution of meromorphic functions. This theory originated over ninety years ago and still plays a very important role in the study of solutions of linar/non-linear differential equations in the complex domain. This thesis is divided into introduction and two chapters. In the rst chapter, we shall adopt the standard notations in Nevanlinna s value distribution theory of meromorphic functions. For example, the characteristic function T (r; f ), the counting function of the poles N (r; f ), and the proximity function m(r; f ) (see, [4],[3]). We use (f ) to denote the order of growth of f and (f ) to denote the exponent of convergence of zeros of f . The rst and the second fundamental theorems are main parts of the theory. The rst main theorem gives an upper bound for the counting

1 function N for any a 2 C and for large r, while the second main theorem r; f a provides a lower bound on the sum of any nite collection of counting functions

1 where a 2 C and large r. In addition the identity