Reasearch On Solution And Related Questions Of Differential Equations And Q-Difference Equations

In this paper, using the Nevanlinna theory of the distribution of meromophicfunctions and the investigation skills of complex differential equations, we investigatethe problem of the existense of admissible solutions of a type of algebraic equations,the value distribution of q-difference polynomials and the meromorphic solutions ofcertain q-difference equations. Some results are improved and generalized. This thesisis divided into four parts:The first part mainly introduced the foundation knowledge of Nevanlinna valuedistribution theory including usual notation, definitions and fundamental theorem.Also, we introduced some fundamental theorem of the q-difference.The second part, the existense of admissible solutions of a type of algebraicequations of a class of complex high order differential equations is discussed, Someresults are improved and generalized, obtained the similar results.The third part discussed the zero point of a class of complex q-differentialpolynomial, obtained the similar results with difference polynomials.The fourth part discussed the solutions of a class of complex q-differenceequation, obtained some results.