几类复线性微分、差分方程解的增长性和值分布
发布时间：2018-09-04 15:21
【摘要】：本文主要运用Nevanlinna值分布理论和整函数的渐近值理论,研究了几类复线性微分、差分方程解的增长性和值分布.全文共分四章.第一章,简要介绍复线性微分方程领域和复差分方程领域的发展历史及本文的研究背景,并介绍了本论文所需的相关定义和常用记号.第二章,研究了一类二阶线性微分方程f" +A1(2)f' A0(z)f = 0解的增长性.假设A1(z)=h1eQ1(z)+ h2eQ2(z),其中Qj(z)(j = 1,2)为n(1)次多项式且首项系数幅角相同,hj为级小于n的整函数,A0为满足下级μ(A0)≠n的超越整函数,得到上述方程的每个非零解都具有无穷级,同时对解的超级进行了估计.第三章,运用Nevanlinna值分布理论和整函数的渐近值理论,研究了一类整函数系数高阶线性微分方程解的增长性.当上述方程有一个系数为满足Denjoy猜想极值情况的整函数时,给出了其每个非零解都为无穷级的判定条件.第四章,研究了一类亚纯系数线性差分方程An(z)f(z + cn)+…+A1(z)f(z + c1)+ A0(z)f(z)= 0和An(z)f(z + cn)+…+ A1(z)f(z + c1)+ A0(z)f(z)= F(z)亚纯解的增长性和值分布,其中Aj(z)=Pj(eA(z))+ Qj(e-A(z))+Rj(z)(j =0,1,…,n),Rj.(z),F(z)(≠ 0)为亚纯函数，，Pj(z),Qj(z),A(z)为多项式.
[Abstract]:In this paper, the growth and value distribution of solutions for some complex linear differential and difference equations are studied by using the Nevanlinna value distribution theory and the asymptotic value theory of the entire function. The full text is divided into four chapters. In the first chapter, the development history of complex linear differential equations and complex difference equations and the background of this paper are briefly introduced, and the relevant definitions and commonly used notations in this paper are also introduced. In chapter 2, we study the growth of solutions of a class of second order linear differential equations f "A1 (2) f'A 0 (z) f = 0. Assuming that A 1 (z) h 1e Q 1 (z) h2eQ2 (z), where Qj (z) (j = 1Q 2) is a polynomial of degree n (1) and the first coefficient is of order less than n with the same amplitude, the entire function A 0 is a transcendental whole function satisfying lower order 渭 (A 0) 鈮
本文编号：2222568
[Abstract]:In this paper, the growth and value distribution of solutions for some complex linear differential and difference equations are studied by using the Nevanlinna value distribution theory and the asymptotic value theory of the entire function. The full text is divided into four chapters. In the first chapter, the development history of complex linear differential equations and complex difference equations and the background of this paper are briefly introduced, and the relevant definitions and commonly used notations in this paper are also introduced. In chapter 2, we study the growth of solutions of a class of second order linear differential equations f "A1 (2) f'A 0 (z) f = 0. Assuming that A 1 (z) h 1e Q 1 (z) h2eQ2 (z), where Qj (z) (j = 1Q 2) is a polynomial of degree n (1) and the first coefficient is of order less than n with the same amplitude, the entire function A 0 is a transcendental whole function satisfying lower order 渭 (A 0) 鈮
本文编号：2222568
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