Research On Some Properties Of Solutions Of Fermat Type Complex Differential-difference Equations

The properties of the solutions of Fermat type differential-differe-nce equations in complex domains are studied by using the Nevan-linna theory and the difference simulation,including the existence and growth of solutions of these equations.This thesis is divided into four chapters.In Chapter 1,we mainly introduce the history of development and research status of complex differential-difference equation and Fermat type functional equation.In addition,some important con-clusions and notations in Nevanlinna theory and difference simula-tion are introduced.The existence and growth of solutions of Fermat type complex differential-difference equations are studied,motivated by the work of Liu-Yang^[43]and Qin^[49].Furthermore,the existence of the solu-tions of transcendental entire functions for two certain more complex Fermat type differential-difference equations is considered inspired by Chen-Lin^[9]in Chapter 2.The existence of the solutions of entire function of the two certain complex differential-difference equations is considered,in which the existence conditions of the solutions are given in Chapter 3.In Chapter 4,on the one hand,the research work of thesis is sum-marized.On the other hand,the future research work is prospected,and two research questions are specifically proposed.