Growth And Value Distribution Of Meromorphic Solutions Of Complex Linear Equations And Complex(Differential-) Difference Polynomials

In this thesis,we mainly use Nevanlinna theory and its difference analogues to inves-tigate the properties of meromorphic solutions of some kinds of complex linear equations and complex(differential-)difference polynomials,which generalize and improve the ones in the previous results.We divide this thesis into three chapters.In Chapter 1,we simply introduce the development history,relative to our main results in this paper,in the field of complex differential equations and in the field of complex differences and complex difference equations.We also give some basic definitions and standard notations on meromorphic functions in the complex plane and in the unit disc;In Chapter 2,we investigate the growth and the value distribution of meromor-phic solutions of some kinds of complex linear equations.Firstly,we investigate the growth and the value distribution of meromorphic solutions of a kind of second-order non-homogeneous complex linear differential equation in the unit disc,and obtain the relationships between the exponents of convergence of meromorphic solutions and their arbitrary-order derivatives taking small function values and the orders of coefficients.Secondly,we investigate the growth of meromorphic solutions of a kind of higher-order homogeneous and non-homogenous complex linear equations for composite functions in the complex plane,and obtain some precise estimates on the lower bound of the order or the lower order of meromorphic solutions,consequently generalize into the more general case of complex linear differential equations for composite functions.In Chapter 3,we investigate the value distribution of some kinds of(differential-)difference polynomials of meromorphic functions.Firstly,we investigate fixed points of meromorphic functions and their higher-order differences and shifts,and obtain the relationships between fixed points of meromorphic functions and the ones of their higher-order differences and shifts,consequently generalize the case of fixed points into the more general case.Secondly,we investigate the zeros of some difference polynomials and differential-difference polynomials of transcendental entire functions of finite order,and obtain the precise estimates on the exponent of convergence of zeros of these polynomials,which can be seen as(differential-)difference analogues of Hayman's classical results on Picard s exceptional values.