系數為缺項冪級數微分方程的復振蕩性質

1、分 類 號： 0174.5 密 級：學校代碼： 10414 學 號：2009010854碩士研究生學位論文系數為缺項冪級數微分方程的復振蕩性質 系數為缺項冪級數微分方程的復振蕩性質Complex Oscillation of Higher Order Linear DifferentialEquations with Coefficients being Lacunary Series江 杰院 所：數學與信息科學學院 導師姓名：涂金副教

2、授學科專業(yè)：應用數學 研究方向：復方程二○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