Several Studies On The Complex Partial Delay-differential Equations

Complex partial differential difference equation(PDDE),which contains both partial differential operator and partial difference operator,is a high-dimensional extension of delay differential equation.Nevanlinna theory is a powerful tool for studying complex equations.In recent years,many scholars have studied the admissible solutions of complex partial differential equations and complex partial differential equations,and have achieved some good results through Nevanlinna theory.For example,Tu Z H,Hu P C and Yang C C independently investigated the existence of meromorphic solutions of complex partial differential equations related to the classical Malmquist type of one variable;Gao L Y gave some results on the admissible meromorphic solutions of systems of complex partial differential equations.Recently,Wang Y and Zhang Q C obtained Malmquist theorems on the admissible meromorphic solutions of systems of complex partial difference equations.My tutor Cao T B and Korhonen R investigated the value distribution of q-differences of meromorphic functions in several complex variables and obtained some results on meromorphic soltions of partial q-difference equations,which provides a theoretical basis for us to propose a universal equation form.In this paper,we show a sufficient condition on the existence of admissible meromorphic solutions of system of complex partial delay differential equations by Nevanlinna theory of meromorphic functions in several complex variables.Some examples are given to suppose our result.In chapter 1,we briefly introduce the research background and main goal of this thesis.In chapter 2,we introduce some preliminary knowledge of this paper,that is,the theory of single-variable and high-dimensional value distribution and many references for studying meromorphic functions.In chapter 3,we studied the admissible meromorphic solutionsof systems of a normal complex delay differential equations.In chapter 4,the main purpose is to study delay differential equations w(z+1,t)+a(z,t)((?)w(z,t)/(?)t)=0,We give the uniqueness of its meromorphic solution.In chapter 5,we obtain the expectations based on our results.