發(fā)布時(shí)間：2018-05-02 18:20

  本文選題：復(fù)線性微分方程 + 復(fù)線性差分方程　； 參考：《江西師范大學(xué)》2015年碩士論文

【摘要】：本文運(yùn)用Nevanlinna值分布理論及其差分模擬結(jié)果研究了復(fù)差分多項(xiàng)式與復(fù)線性微分、差分方程亞純解的一些性質(zhì),改進(jìn)并完善了前人的結(jié)果.全文分為三章.第一章,簡(jiǎn)要介紹了復(fù)線性微分方程領(lǐng)域和復(fù)差分與復(fù)差分方程領(lǐng)域的發(fā)展歷史和本文主要內(nèi)容,并介紹了復(fù)平面上和單位圓內(nèi)亞純函數(shù)的一些定義和常用記號(hào).第二章,在復(fù)平面上和單位圓內(nèi)研究了幾類(lèi)復(fù)線性微分方程亞純解的增長(zhǎng)性和值分布.分別在復(fù)平面上和單位圓內(nèi)研究了一類(lèi)具某種特殊解析函數(shù)系數(shù)的齊次線性微分方程解的迭代級(jí)；在復(fù)平面上研究了一類(lèi)具Fabry缺項(xiàng)級(jí)數(shù)系數(shù)或具慢增長(zhǎng)性解析函數(shù)系數(shù)的非首1齊次和非齊次線性微分方程亞純解的級(jí)、超級(jí)和解取小函數(shù)值點(diǎn)的收斂指數(shù)、超收斂指數(shù)；在單位圓內(nèi)研究了一類(lèi)具慢增長(zhǎng)性解析函數(shù)系數(shù)的齊次和非齊次線性微分方程解的級(jí)、M-級(jí)、超級(jí)和超M-級(jí).第三章,運(yùn)用Nevanlinna理論的差分模擬結(jié)果并結(jié)合復(fù)線性微分方程的一些研究方法,研究了復(fù)線性差分方程和復(fù)線性微-差分方程亞純解及復(fù)差分多項(xiàng)式的增長(zhǎng)性和值分布.研究了一類(lèi)具相同增長(zhǎng)級(jí)系數(shù)的齊次線性差分方程亞純解的級(jí)和解取小函數(shù)值點(diǎn)的收斂指數(shù)；分別研究了多項(xiàng)式系數(shù)、超越整函數(shù)系數(shù)、亞純函數(shù)系數(shù)的齊次和非齊次線性微-差分方程亞純解的級(jí)和下級(jí)；研究了有限級(jí)整函數(shù)的差分多項(xiàng)式的零點(diǎn)、取小函數(shù)值點(diǎn)和Borel例外值點(diǎn)分布.
[Abstract]:In this paper, some properties of meromorphic solutions of complex difference polynomials and complex linear differential and difference equations are studied by using Nevanlinna value distribution theory and their difference simulation results. The full text is divided into three chapters. In the first chapter, the development history of complex linear differential equations and complex difference and complex difference equations and the main contents of this paper are briefly introduced, and some definitions and commonly used notations of meromorphic functions in complex plane and unit circle are also introduced. In chapter 2, we study the growth and value distribution of meromorphic solutions of some complex linear differential equations on the complex plane and in the unit circle. The iterative order of the solutions of a class of homogeneous linear differential equations with some special analytic function coefficients is studied on the complex plane and in the unit circle respectively. In this paper, we study the order of meromorphic solutions of a class of nonhomogeneous and nonhomogeneous linear differential equations with the coefficients of Fabry deficient series or analytic functions with slow growth on the complex plane. In this paper, we study the order M- order, super and super M- order of solutions of homogeneous and nonhomogeneous linear differential equations with slowly growing analytic function coefficients in a unit circle. In chapter 3, the growth and value distribution of meromorphic solutions and complex difference polynomials of complex linear difference equations and complex linear differential equations are studied by using the difference simulation results of Nevanlinna theory and some research methods of complex linear differential equations. In this paper, we study the convergence exponents of meromorphic solutions of homogeneous linear difference equations with the same growth order coefficients, and study the coefficients of polynomial and transcendental functions, respectively. The order and lower order of meromorphic differential equation with homogeneous and inhomogeneous linear differential-difference equations are studied, the zero points of difference polynomial of finite order integral function are studied, and the distribution of small function value points and Borel exceptional value points are obtained.
【學(xué)位授予單位】：江西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O174.52
，

本文編號(hào)：1834979