Research On Properties Of Meromorphic Solutions Of Complex Difference Equations

In this article, we investigate the properties of the growth order of transcendental meromor-phic solutions of homogenous and nonhomogeneous linear difference equations, the properties of entire solutions of a certain of difference equation, and the properties of meromorphic solu-tions with a direct tract. The full text is divided into three chapters.In Chapter 1, we outline some basic concepts, results and notations of Nevanlinna value distribution theory; the Nevanlinna Characteristic, the results of difference Navenlinna theories; the definition and results of direct tract.In Chapter 2, we first research the properties of meromorphic solutions of nonhomoge-neous linear difference equation and the corresponding homogeneous linear difference equation, which improve the conclusions of Chen . When the coefficients are polynomials and entire functions respectively, for any small functions ? of f, we get some relations of the exponent of convergence of zeros, poles of f-? and the order of growth of transcendental meromorphic solutions of complex linear difference equations. We also study the properties of meromorphic solutions of the difference equation if the coefficients are entire functions and satisfy some certain conditions, which promote the results of Yia-Man Chiang and Shao-Ji Feng .In Chapter 3, we first research the properties of the entire solutions of difference equation with 0< ?(f)< 1. When the difference operator ?if(z) of the equation is replaced with f(z+i), then we continue to investigate the finite order of entire solutions of this difference equation. And we research the properties of meromorphic solutions with a direct tract of equations Finally, we study the difference polynomial of meromorphic functions f(z) with finitely many poles and get the result of zeros with the order of solutions less than 1.