Complex Differential-difference Equations Of Meromorphic Solutions And Related Problems

Using Nevanlinna theory of the value distribution of meromorphic functions oralgebroid functions, this paper maily investigates the problem of the value distributionof meromorphic admissible solutions of higher-order differential equations, the valuedistribution of the algebroid solutions of a kind of higher-order algebraic differentialequations and the growth order of solutions of systems of complex differenceequations. Some results are improved and generalized. This paper is divided into fivechapters:In chapter one, we describe the elementary knowledge of Nevanlinna theory ofmeromorphic function and algebroid function, including related concepts and fundam-ental theorems.In chapter two, using Nevanlinna theory of the value distribution of meromorp-hic functions, the problem that the existence of solutions of the complex higher-orderdifferential equation is disscussed. And under the assumption of certain propercondition, we prove a result which the meromorphic solutions of the differentialequation must be non-admissible solutions. At the end of this paper, the examples aregiven to show that the result is precise.In chapter three, using Nevanlinna theory of the value distribution of meromor-phic functions or algebroid functions, the problem of the value distribution ofalgebroid solutions of some algebraic differential equations is investigated. Thedeficient values of a type higher-order algebraic differential equations are obtained oncondition that the equations exist admissible algebroid solutions and meet someproper conditions.In chapter four, the form of a class of a systemof complex differential equationswith admissible solutions is investigated, and some results different from singledifferential equation are obtained.In chapter five, using Nevanlinna theory of the value distribution of meromorp-hic functions, the problem of growth order of solutions of a class of system of compl- ex difference equations is investigated, some results are improved and generalized.And extend some results of the growth order of solutions of system of differentialequations to difference equations.