Some Researches On Solutions Of Complex Differential-Difference Equations And Complex Difference Equations

In this paper,we mainly uses the theory of value distribution of meromorphic functions and the theory of difference simulation as the main tools of research,this dissertation studies the transcendental meromorphic(entire)solutions of a certain type of complex differential-difference equations and Pielou Logistic equation with entire function coefficients with the finite order of growth.Paper is divided into four chapters,the concrete arrangement is as follows.In Chapter 1,we mainly introduce the research background and content of this paper in the introduction.We mainly introduce some basic notations and the results on the value distribution theory of meromorphic functions and the difference version of Nevanlinna theory in the preliminary knowledge.In Chapter 2,we generalize a certain type of nonlinear complex differential-difference equations.We analyze and obtain the order of growth and the exponent of convergence of zeros of the transcendental entire solution and the existence of the exponential polynomial solution.In Chapter 3,the Pielou Logistic equation with polynomial coefficients is extended to the case where this equation with finite-order entire function coefficients.When only one of the coefficients of the equation has the maximum order of growth and this equation satisfies certain conditions,we can obtain the lower bound of the order of growth of the transcendental meromorphic solutions and some value distribution properties of the solutions,which enriches and perfects some original results.In Chapter 4,we mainly make a summary and follow-up work.