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

In this paper,we mainly use Nevanlinna value distribution theory and its difference ana-logues to study some properties of meromorphic sulutions of some kinds of complex linear(differential-)difference equations,and obtain some results generalizing the previous results.We divide this paper into three chapters.In Chapter 1,we simply introduce the development history of complex linear differential equations and complex linear difference equations and main contents in this paper,and give some definitions and notations on meromorphic functions in the complex plane.In Chapter 2,we investigate the ralations between the growth of coefficients and the growth of mcroinorphic solutions of general complex linear differential-difference equation,and obtain the estimates on the lower bound of the order of meromorphic solutions by comparing the(lower)orders or the(lower)types of the coefficients.Our results can be seen as generalizations for both the case of complex linear differential equation and the case of complex linear difference equation.In Chapter 3,we investigate a kind of second-order homogeneous and non-homogeneous complex linear difference equations,and obtain the estimates on the growth of linear difference polynomials generated by meromorphic solutions of the involved equations,and the estimates on the value distribution of these linear difference polynomials taking the value of small func-tions.Moreover,as the applications of the above results,we investigate the growth and the value distribution of first and second order difference operators of meromorphic solutions of the involved equations.