APPLICATIONS OF THE NEVANLINNA THEORY IN THE STUDY OF COMPLEX FUNCTIONAL EQUATIONS

Abstract

This thesis focuses on Nevanlinna's theory of difference and its applications in the study of complex functional equations. We are interested in some problems related to the growth of solutions of difference equations and also to differential difference equations in general. The substance of these studies is found in the recent counterparts of Nevanlinna's difference theory. The key result is the lemma of the logarithmic derivative in difference form obtained recently by Halburd-Korhonen and Chiang- Feng, independently.