The Entire Solutions Of A Certain Type Of Non-linear Q-difference Equation

Recently,many scholars engaged with the study on solvability and existence of solutions of non-linear difference equations.This study is also one of those studies,we try to investigate the entire solutions and study the existence of entire solutions of the non-linear difference equations of the form fn(z)+Q(z)f(qz)=p1(z)e?z+p2(z)e-?z,where Q(z),p1(z)p2(z)are non-zero polynomials and q,? are non-zero constants.This study is based on f(qz)term.Therefore we have o use q-difference analogue of the Logarithmic Derivative Lemma.This lemma was proved by Barnett,cannot be extended to hold for all finite-order meromorphic functions.This dissertation consists of four parts and the including are as follows.Chapter 1 entitled"Introduction" give a brief introduction to Nevanlinna the-ory,including some basic definitions which are well known with commonly used symbols and some important tools,results.In chapter 2,e discuss about some invaluable tools for q-difference equa-tions like q-difference analogue of the lemma on the logarithmic derivative and q-difference analogue to Clunie lemma.In chapter 3,we discuss about the important theorems and lemmas for the study and we investigate the entire solutions for the above form of equations.Chapter 4 includes conclusions and prospects.