Some Properties Of Solutions Of Complex Difference And Differential Equations

The theory of value distribution is considered the greatest achievements of research field of meromorphic functions in the last century. It was founded by R.Nevanlinna in 1920 s. The theory has always been developing, and is widely used in the research of complex differential and complex difference equations. By using the theory of value distribution, we investigate some properties of complex difference and differential equations in this dissertation. The main novelties and results are briefly stated below. In chapter 3, we consider the value distribution of differenceφ₁（z）=f（z+c）/（f（z））^k-a（f（z））ⁿ and φ₂（z）=（m|∏）i=1f（z+c_i）/（f（z））^k-a（f（z））ⁿ From the viewpoint of Nevanlinna theory, we obtained some results in analogy with Picard Theorem. In chapter 4, we shall investigate the growth of solutions offⁿ+A₁（z）e^azf’+（m|∑）j=1(B_j（z）e^b_jz)=0 By using the Nevanlinna theory of meromorphic functions, we obtain some precise estimates of growth of solutions of the above equations which are improvements of the previous results due to Chen.