Properties On The Solutions Of Types Of (System Of) Complex Differential-difference Equations

Based on the Valiron theory of entire function,the Nevanlinna value distribution theory of meromorphic function and some skills of complex differential(difference)equations,we investigate the zeros of polynomials with transcendental meromorphic solution on a type of(system of)complex differential equations,the value distribution of algebroid solutions of a type of higher order differential equations and also study the form of meromorphic solutions of some types of systems of difference equations.Some results of references are improved and generalized.Examples show that our results are precise.This thesis is divided into six chapters:The first chapter mainly introduces the foundation knowledge of Nevanlinna value distribution theory including usual notations,definitions and fundamental theorems.Also,we introduce some fundamental theorems of the algebroid function equations and difference equations.The second chapter we investigate the zeros of polynomials with transcendental meromorphic solution of a type of(system of)complex differential equations.Two results are obtained,and the discussion of system of differential equations is based on the result of differential equations.Examples show that the upper bounder or lower bounder in conditions can be reached.The third chapter we discuss the value distribution of algebroid solutions of a type of systems of higher order differential equations.The deficient values of a type higher order algebraic differential equations are obtained on condition that the equations exist admissible algebroid solutions and meet some proper conditions.Some results in references are the special cases of theorems in this chapter.The fourth chapter we investigate the existence form of a type of complex difference equations,under the assumption restricted to certain proper conditions,some results are obtained,which extend the results of difference equations to the systems of difference equations.And examples show that our conditions are precise.The fifth chapter we discuss the form of transcendental meromorphic solutions of a type of complex difference-differential equations.Improvements and extensions of some results in references are presented.And examples show that our results are true.The sixth chapter we investigate the properties of transcendental solutions of(systems of)composite functional equations,characteristic estimate and non-integrated counting estimate of solutions are obtained while restricting the number of the poles of the coefficients.Examples show that our condition in Theorems are precise.