The Value Distribution Theory And Related Questions Of Difference Equations

In this paper, using the Nevanlinna value distribution theory of meromorphic functionand some skills of complex differential equations, we investigate the problems of thevalue distribution of differential polynomials, the existence and the order of meromorphicsolutions of some systems of algebraic differential equations, and the existence ofmeromorphic solutions of difference equations. This thesis is divided into five parts:The first part, we describe the basic Nevanlinna theory of meromorphic function andalgebroid function, including fundamental definitions and fundamental theorems, we alsointroduced some fundamental theorem of the difference.The second part, using the Nevanlinna value distribution theory of meromorphicfunction，we investigate the problems of zeros of differential polynomials, improve someprevious results of Yihongxun etc.The third part, using the Nevanlinna value distribution theory of meromorphicfunction, we investigate the problems of the relations of deficient and deficiency of themulti-valued entire algebroid functions.The fourth part, using the Nevanlinna value distribution theory of meromorphicfunction and algebroid function theory, we discuss the problem of the growth of solutionsof higher-order algebraic differential equations.The five part, using the Nevanlinna value distribution theory of meromorphic functionand fundamental theorem complex difference equations,we discuss meromorphicsolutions of nonlinear difference equations, improve some previous results, and examplesshow that our conclusions are better.