Research On Uniqueness Of Complex Differential-difference Polynomials And Distribution Of Solutions Of Complex Differential-difference Equations

Applying the Nevanlinna theory in studying solutions of complex differential equations and uniqueness of polynomials is an important tropic in complex analysis.In this essay, we mainly discuss the problem of distribution of solutions of nonlinear differential equations and linear differential-difference equations by using difference analogue of Nevanlinna theory, also consider the uniqueness of a transcendental entire function with its linear mixed differential-difference operators under a shared value or a small function. We arrange this essay as follows.In chapter 1. We introduce the important backgrounds and main works of this essay.In chapter 2. We introduce the Nevanlinna theory and its difference analogue theory.In chapter 3. We study the uniqueness problem of a transcendental entire function f(z) with its differential-difference polynomials and of two differential-difference polynomials under a shared value or a small function, we also consider the uniqueness problem of f(z) with its complex linear differential-difference operators under a shared value or a small function.In chapter 4. We study the relation between the order of growth of solutions and exponent of convergence of zeros of solutions of complex linear and nonlinear differential-difference equations.In chapter 5. With regard to some given results, we present some open problems as our further studying.