Growth Of Meromorphic Solutions Of Homogeneous And Non-homogeneous Complex Linear Differential Equations And Complex Linear (Differential-) Difference Equations In The Complex Plane

In this thesis,we mainly use Nevanlinna theory and its difference analogues to investigate the growth of meromorphic solutions of complex linear differential equations and complex linear(differential-)difference equations,and obtain some results improving and generalizing the previous results.We divide this thesis into four chapters.In Chapter 1,we simply introduce the development history in the field of complex linear differential equations and in the field of complex linear difference equations.We also introduce the main content of this thesis and give some definitions needed in this thesis.In Chapter 2,by combining the definition and properties of Fejer gap series,we investigate a kind of the homogeneous and non-homogeneous complex linear differential equation.When some one of the coefficients is relative to Fejer gap series and the other coefficients are entire or meromorphic functions,the estimates on the order of meromorphic solutions of the involved equation are obtained,which improve the previous results.In Chapter 3,by combining the difference analogues of Nevanlinna Theory and us-ing some methods in the field of complex linear differential equations,we investigate a kind of non-homogeneous complex linear difference equations with special meromor-phic coefficients.When there exist admit more than one coefficient having the same maximal order and the same maximal type,the estimates on the lower bound of the order of meromorphic solutions of the involved equations are obtained.Meanwhile,the above estimates are sharpened by combining the relative results of the corresponding homogeneous complex linear difference equations.In Chapter 4,we investigate a kind of the homogeneous and non-homogeneous complex linear difference equation and generalize the equation into the case of complex linear differential-difference equation.When there exists only one coefficient having the maximal iterated order or having the maximal iterated type among those having the maximal iterated order,and the above coefficient satisfies certain conditions on its poles,the estimates on the lower bound of the iterated order of meromorphic solutions of the involved equations are obtained.Meanwhile,the case for p = 1 is also discussed and corresponding results are obtained by strengthening some conditions.In the end,some examples are given to illustrate the sharpness of the results.