The Growth Of Solutions Of Complex Differential Equations And The Value Distribution Of Meromorphic Solutions Of Difference Equations

In this paper, we investigated oscillation of solutions of linear differential equations and value distribution of meromorphic solutions of homogeneous linear difference equations by using value distribution theory of Nevanlinna and difference analogue of the lemma on the logarithmic derivative. There are four chapters in this thesis.In Chapter 1, we first introduce the research of linear differential equations and linear difference equations. Then narrates some definitions and knowledge used frequently are given to readers in this chapter.In Chapter 2, we mainly investigate the growth of solutions of second order linear differential equation f"+Af’+Bf=0 with different coefficients by using value distribution theory in angular domain. Assume that A(z)= h(z)eP1(z) be an entire function, where P1 (z) is a polynomial with degree m and h(z) is an entire function of order p(h)<m, or assume that A(z) be a nontrivial solution of f"+P2(z)f=0, where P2(z) is a polynomial with degree n. we can obtained every nontrivial solution of second order linear differential equations is of infinite order.In Chapter 3, we investigate the growth of solutions of the higher order linear differential equations by using the fundamental theory and method of value distribution of Nevanlinna. Assume that one of coefficients extreme for Yang’s inequality, we can obtained solution f(?)0 of the complex differential equation has infinite order.In Chapter 4, we investigate value distribution of meromorphic solutions of difference equations in terms of deficient value. Assume that one of coefficients has deficient value or control action in angular domain, we can obtained accurate estimation of meromorphic solutions of difference equations and exponent of convergence of non-zero-sequence a.