復(fù)平面及單位圓內(nèi)線性微分方程的解及其空間屬性
發(fā)布時間：2019-04-24 14:24
【摘要】：本文應(yīng)用Nevanlinna值分布理論和方法,研究了幾類復(fù)域微分方程的解的性質(zhì)。全文共分為以下四章。第一章,簡要介紹了微分方程復(fù)振蕩理論的研究現(xiàn)狀,以及本文的研究背景,并引入了一些相關(guān)的記號和定義。第二章,研究了一類二階非齊次線性微分方程解的一些性質(zhì),得到上述方程的解的級與超級的估計,同時還研究了該方程解的不動點的性質(zhì),完善了已有結(jié)果.第三章,研究了二階齊次線性微分方程的解,其中是關(guān)于z的多項式.當(dāng)多項式的系數(shù)為超越整函數(shù)時,得到了超級的精確估計.第四章,研究了一類高階線性非齊次微分方程在單位圓中解的性質(zhì),得到了方程的解所在的空間性質(zhì).
[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.
【學(xué)位授予單位】：江西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O174.52
本文編號：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.
【學(xué)位授予單位】：江西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O174.52
【參考文獻】
相關(guān)期刊論文 前3條
1 陳宗煊;一類單位圓內(nèi)微分方程解的性質(zhì)[J];江西師范大學(xué)學(xué)報(自然科學(xué)版);2002年03期
2 王錦熙;易才鳳;徐洪焱;;關(guān)于單位圓內(nèi)高階線性微分方程的復(fù)振蕩[J];江西師范大學(xué)學(xué)報(自然科學(xué)版);2009年02期
3 陳宗煊;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
，本文編號：2464522
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