Some Properties Of Meromorphic Solutions Of Complex Linear Differential、Difference Equations And Complex Difference Polynomials

In this thesis, we mainly use Nevanlinna theory and its difference analogues to in-vestigate some properties of complex difference polynomials and meromorphic solutions of complex linear differential and difference equations, and obtain some results comple-menting and improving the previous results. We divide this thesis into three chapters.In Chapter 1, we simply introduce the development history in the field of complex linear differential equations and in the field of complex differences and complex difference equations, as well as main contents of this thesis. We also give some definitions and normal notations on meromorphic functions in the complex plane and in the unit disc.In Chapter 2, we investigate the growth and value distribution of meromorphic solutions of some kinds of complex linear differential equations in the complex plane and in the unit disc. In detail, we investigate the iterated order of solutions of a homogeneous linear differential equation with specific analytic coefficients in the complex plane and in the unit disc respectively; we investigate the order, the hyper order, the convergence exponent and the hyper convergence exponent of the sequence of small function value points of meromorphic solutions of non-monic homogeneous and non-homogeneous linear differential equations with coefficients being Fabry gap series or slow growth analytic functions in the complex plane; we also investigate the order, the M-order, the hyper order and the hyper M-order of solutions of homogeneous and non-homogeneous linear differential equations with coefficients being slow growth analytic functions.In Chapter 3, we investigate the growth and value distribution of complex differ-ence polynomials and meromorphic solutions of complex linear difference equations and complex linear differential-difference equations, by making use of difference analogues of Nevanlinna theory and combining some research methods in the field of complex linear differential equations. In detail, we investigate the order and the convergence exponent of the sequence of small function value points of meromorphic solutions of homogeneous linear difference equations with coefficients having the same order; we investigate the or-der and the lower order of meromorphic solutions of homogeneous and non-homogeneous linear differential-difference equations with coefficients being polynomials, transcendental entire functions and meromorphic functions respectively; we also investigate the distri-bution of zeros, small function value points, and Borel exceptional points of difference polynomials of entire functions with finite order.