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

In this thesis,we mainly use Nevanlinna theory and its difference analogues to inves-tigate the properties of meromorphic solutions of complex linear differential,difference,and differential-difference equations,which complement and improve the ones in the previous results.We divide this thesis into three chapters.In Chapter 1,we simply introduce the development history of complex linear differ-ential equations and complex linear difference equations,and 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 meromorphic solutions of some kinds of complex linear differential equations in the complex plane and in the unit disc.Firstly,we investigate a kind of second order homogeneous linear differential equation in the complex plane,and obtain the relations between the order of meromorphic solutions,the convergence exponents of(distinct)zeros and(distinct)poles of meromorphic solutions and the order of the coefficients when the coefficients are meromorphic functions with[p,q]-? order and satisfy certain conditions;Secondly,we investigate a kind of higher order non-homogeneous linear differential equation in the unit disc,and obtain the estimates on the convergence exponents of distinct zeros of any two linearly independent meromorphic solutions when A0(z)is the dominating coefficient and has infinite regular order,which generalize the corresponding results in the complex plane.In Chapter 3,we investigate the growth and the value distribution of meromor-phic solutions of some kinds of complex linear(differential-)difference equations.Firstly,we investigate a kind of complex linear difference equation with entire or meromorphic coefficients,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,which generalize the corresponding results of complex linear differential equations;Secondly,we investigate a kind of homogeneous and non-homogeneous complex linear differential-difference equation with meromorphic coefficients,and obtain the relations between the order of meromorphic solutions and the convergence exponents of the zeros,poles,a-points,small function value points of meromorphic solutions,showing the relations in the case of non-homogeneous equations are sharper than the ones in the case of homoge-neous equations,which generalize the corresponding results of complex linear differential equations and complex linear difference equations.