The Properties Of Solutions Of Some Types Of Complex Differential-Difference Equations

Using the Nevanlinna value distribution theory of meromorphic function and algebroid function,complex differential(difference)equations theory,as well as some techniques,we discuss the existence of algebroid solutions,meromorphic solutions and representation of solutions of some types of complex differential(difference)equations.Considering that the properties of the solution of the equation are not necessarily suitable for the system of equations,the zeros of a type of system of second order complex differential equations is also discussed.This thesis is divided into five chapters:The first chapter mainly introduces the relevant content of Nevanlinna value distribution theory.Moreover,some fundamental theorems of complex difference equations are introduced.The second chapter we discuss the properties of one type of non-linear differential-difference equation with rational solution,and the existence of transcendental meromorphic solutions of another type of equation.Some corresponding results are obtained.The third chapter we investigate the existence of algebroid solutions of a type of higher-order algebroid differential equation on condition that the degree of solutions meet some proper conditions,and we obtain three equivalent propositions of deficiency and exceptional values in the case of algebroid solution.Some results in previous paper are extended,that is,the theorem is more universal compared with the previous conclusions.Examples show that our conditions in Theorems are precise.The fourth chapter we discuss the properties and expression of meromorphic solutions of a type of complex differential-difference equation.The result is similar to the complex difference equation.Example proves that the conclusion of the theorem is meaningful.The fifth chapter we investigate the problem of the zeros of polynomials of a type of systems of second-order algebraic differential equations with transcendental meromorphic solutions.Two results are obtained.