系數(shù)為缺項(xiàng)冪級(jí)數(shù)微分方程的復(fù)振蕩性質(zhì)

1、分 類 號(hào)： 0174.5 密 級(jí)：學(xué)校代碼： 10414 學(xué) 號(hào)：2009010854碩士研究生學(xué)位論文系數(shù)為缺項(xiàng)冪級(jí)數(shù)微分方程的復(fù)振蕩性質(zhì) 系數(shù)為缺項(xiàng)冪級(jí)數(shù)微分方程的復(fù)振蕩性質(zhì)Complex Oscillation of Higher Order Linear DifferentialEquations with Coefficients being Lacunary Series江 杰院 所：數(shù)學(xué)與信息科學(xué)學(xué)院 導(dǎo)師姓名：涂金副教

2、授學(xué)科專業(yè)：應(yīng)用數(shù)學(xué) 研究方向：復(fù)方程二○一二年六月AbstractIn this thesis, we make use of the basic knowledge of theory of complexlinear differential equations to investigate complex oscillation of higher order lineardifferential equations with

3、coefficients being lacunary series. This thesis is madeup of three chapters.In chapter 1, we introduce the definitions and some basic notations aboutcomplex linear differential equations and some basic theory of Nevanlin

4、na valuedistribution theory of meromorphic functions.In chapter 2, we investigate the growth of the solutions of equation (1.1.1)and (1.1.2) with coefficients being lacunary series of finite order.In chapter 3, we replac

5、e the coefficients of finite order in (1.1.1) and (1.1.2)with lacunary series of finite iterated order and continue to investigate the growthand exponent of convergence of zero sequence of the solutions of equation (1.1.

6、1)and (1.1.2) under some condition, and we obtain some results which improve andextend the results in chapter 2.Keywords higher order linear differential equation, lacunary series, hyperorder, iterated order, exponent of