Research On Solutions Of Complex Differential Equations And Difference Equations

In this paper, using the Nevanlinna theory of the distribution of meromophicfunctions and the skills of complex differential equations, we investigate theadmissible algebroid solutions of some types of nonlinear differential equations andthe growth of the solutions, and also study the admissible meromorphic solutions ofsome types of complex difference equations and systems of complex differenceequations, the meromorphic solutions of some types of complex q-differenceequations and systems of complex q-difference equations, and the growth of solutionsof two types of complex difference-differential equations.Some results of referenceare improved and generalized. Examples show that our results are precise. This thesisis divided into five chapters:The first chapter mainly introduces the foundation knowledge of Nevanlinnavalue distribution theory including usual notation, definitions and fundamentaltheorem. Also, we introduce some fundamental theorem of the difference andq-difference.The second chapter, we study the admissible algebroid solutions of some types ofnonlinear differential equations and the growth of the solutions, and obtain someresults which due to Gao Ling-yun et are in improved and generalized. Examplesshow that the upper bounder or lower bounder in conditions can be reached.The third chapter we discuss the admissible meromorphic solutions of two typesof systems of complex difference equations. Improvements and extensions of someresults in references are presented. Examples show that our conditions andconclusions are precise.The fourth chapter we investigate the problem of existence of meromorphicsolutions of some types of complex q-difference equation and systems of complexq-difference equations, and the similar results with difference polynomials areobtained. Some results in references are the special cases of theorems in this chapter. The fifth chapter discusses the growth of solutions of two types of complexdifference-differential equations, and obtain two results which due to Gao Ling-yunet are in proved and generalized. Examples show that our results are precise.