Several Studies On The Meromorphic Solutions Of Delay Differential Equations

Delay differential equations,that is,equations containing both derivatives and shifts,are also called differential-difference equations.This dissertation studies the growth of complex delay differential equations with integrability(that is,”Painlevéproperty”).We shall use Nevanlinna theory to deal with equations,and generalize the result which was obtained by Halburd and Korhonen in 2017.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 article,such as,preliminary Nevanlinna theory and Value distribution theory with equations.In chapter 3,we study the transcendental meromorphic solutions(with minimal hypertype)of the higher order delay differential equations (?) and (?) where k is a positive integer,a(z)is a rational function,R(z,w)is irreducible-rational in w with rational coefficients.In chapter 4,the main purpose is to study transcendental meromorphic(with min-imal hypertype)solutions of the first order differential equations with delays (?) and (?) ,where k,a(z)and R(z,w)are same as in chapter 3.In chapter 5,we obtain the expectations based on our results.