复平面及单位圆内线性微分方程的解及其空间属性
发布时间：2019-04-24 14:24
【摘要】：本文应用Nevanlinna值分布理论和方法,研究了几类复域微分方程的解的性质。全文共分为以下四章。第一章,简要介绍了微分方程复振荡理论的研究现状,以及本文的研究背景,并引入了一些相关的记号和定义。第二章,研究了一类二阶非齐次线性微分方程解的一些性质,得到上述方程的解的级与超级的估计,同时还研究了该方程解的不动点的性质,完善了已有结果.第三章,研究了二阶齐次线性微分方程的解,其中是关于z的多项式.当多项式的系数为超越整函数时,得到了超级的精确估计.第四章,研究了一类高阶线性非齐次微分方程在单位圆中解的性质,得到了方程的解所在的空间性质.
[Abstract]:In this paper, the Nevanlinna value distribution theory and method are used to study the properties of solutions of several kinds of complex domain differential equations. The full text is divided into the following four chapters. In the first chapter, the research status of the complex oscillation theory of differential equations is introduced briefly, and the research background of this paper is also introduced, and some related marks and definitions are introduced. In the second chapter, some properties of the solutions of a class of second order nonhomogeneous linear differential equations are studied, and the order and super estimates of the solutions of the above equations are obtained. At the same time, the properties of the fixed points of the solutions of the equations are also studied, and the existing results are perfected. In chapter 3, we study the solution of second order homogeneous linear differential equation, where is the polynomial of z. The super accurate estimation is obtained when the coefficients of the polynomial are transcendental whole function. In chapter 4, the properties of the solutions of a class of higher order linear inhomogeneous differential equations in the unit circle are studied, and the spatial properties of the solutions of the equations are obtained.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O174.52
本文编号：2464522
[Abstract]:In this paper, the Nevanlinna value distribution theory and method are used to study the properties of solutions of several kinds of complex domain differential equations. The full text is divided into the following four chapters. In the first chapter, the research status of the complex oscillation theory of differential equations is introduced briefly, and the research background of this paper is also introduced, and some related marks and definitions are introduced. In the second chapter, some properties of the solutions of a class of second order nonhomogeneous linear differential equations are studied, and the order and super estimates of the solutions of the above equations are obtained. At the same time, the properties of the fixed points of the solutions of the equations are also studied, and the existing results are perfected. In chapter 3, we study the solution of second order homogeneous linear differential equation, where is the polynomial of z. The super accurate estimation is obtained when the coefficients of the polynomial are transcendental whole function. In chapter 4, the properties of the solutions of a class of higher order linear inhomogeneous differential equations in the unit circle are studied, and the spatial properties of the solutions of the equations are obtained.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O174.52
【参考文献】
相关期刊论文 前3条
1 陈宗煊;一类单位圆内微分方程解的性质[J];江西师范大学学报(自然科学版);2002年03期
2 王锦熙;易才凤;徐洪焱;;关于单位圆内高阶线性微分方程的复振荡[J];江西师范大学学报(自然科学版);2009年02期
3 陈宗煊;The growth of solutions of f"+e~(-z)f' + Q(z)f = 0 where the order (Q) = 1[J];Science in China,Ser.A;2002年03期
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