【摘要】：本文主要運(yùn)用Nevanlinna值分布理論和整函數(shù)的漸近值理論,研究了幾類復(fù)線性微分、差分方程解的增長(zhǎng)性和值分布.全文共分四章.第一章,簡(jiǎn)要介紹復(fù)線性微分方程領(lǐng)域和復(fù)差分方程領(lǐng)域的發(fā)展歷史及本文的研究背景,并介紹了本論文所需的相關(guān)定義和常用記號(hào).第二章,研究了一類二階線性微分方程f" +A1(2)f' A0(z)f = 0解的增長(zhǎng)性.假設(shè)A1(z)=h1eQ1(z)+ h2eQ2(z),其中Qj(z)(j = 1,2)為n(1)次多項(xiàng)式且首項(xiàng)系數(shù)幅角相同,hj為級(jí)小于n的整函數(shù),A0為滿足下級(jí)μ(A0)≠n的超越整函數(shù),得到上述方程的每個(gè)非零解都具有無窮級(jí),同時(shí)對(duì)解的超級(jí)進(jìn)行了估計(jì).第三章,運(yùn)用Nevanlinna值分布理論和整函數(shù)的漸近值理論,研究了一類整函數(shù)系數(shù)高階線性微分方程解的增長(zhǎng)性.當(dāng)上述方程有一個(gè)系數(shù)為滿足Denjoy猜想極值情況的整函數(shù)時(shí),給出了其每個(gè)非零解都為無窮級(jí)的判定條件.第四章,研究了一類亞純系數(shù)線性差分方程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)亞純解的增長(zhǎng)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)為亞純函數(shù)，，Pj(z),Qj(z),A(z)為多項(xiàng)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

本文編號(hào)：2222568