本文選題：復線性微分方程 + 亞純解��； 參考：《江西師范大學》2015年碩士論文

【摘要】：本文運用Nevanlinna值分布理論分別在復平面上和單位圓內研究了幾類復線性微分方程亞純解的增長性和值分布.同時,還研究了一類q-平移差分-微分多項式的值分布.所得結果是對前人已有結果的推廣和改進.全文分為四章.第一章,扼要介紹了復線性微分方程值分布理論和復差分與差分方程理論的主要發(fā)展線索,同時介紹了本文主要內容和一些基本定義.第二章,在復平面上研究了一類具有Lacunary缺項級數系數的高階齊次和非齊次線性微分方程亞純解的[p,q]級和[p,q]下級及解取小函數值點的[p,q]收斂指數和[p,q]下收斂指數.第三章,在單位圓內研究了系數為亞純函數的齊次和非齊次線性微分方程亞純解的微分多項式取小函數值點的迭代收斂指數和迭代下收斂指數.第四章,研究了一類正有窮級整函數的q-平移差分-微分多項式的值分布.
[Abstract]:In this paper, the growth and value distribution of meromorphic solutions of some complex linear differential equations are studied on the complex plane and in the unit circle by using Nevanlinna value distribution theory. At the same time, the value distribution of a class of q-translation difference differential polynomials is studied. The result is a generalization and improvement of the previous results. The full text is divided into four chapters. In the first chapter, we briefly introduce the value distribution theory of complex linear differential equation and the main development clue of complex difference and difference equation theory. At the same time, we introduce the main contents and some basic definitions of this paper. In chapter 2, we study the [pnq] convergence index and the convergence index under [pnq] and [pnq] of meromorphic solutions of a class of higher order homogeneous and nonhomogeneous linear differential equations with Lacunary deficient series coefficients on the complex plane. In chapter 3, we study the iterative convergence exponents and the convergence exponents of the meromorphic homogeneous differential equations with meromorphic coefficients and the meromorphic solutions of nonhomogeneous linear differential equations at the point of small function in the unit circle. In chapter 4, we study the value distribution of q-translation differential-differential polynomials for a class of positive finite-order entire functions.
【學位授予單位】：江西師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O174.52

【參考文獻】

相關期刊論文 前1條

1 高仕安，，王升，陳宗煊;A　NOTE　ON　THE　COMPLEX　OSCILLATION　OF　NONHOMOGENEOUS　LINEAR　DIFFERENTIAL　EQUATIONS　WITH　TRANSCENDENTAL　ENTIRE　COEFFICIENTS[J];ANNALS OF DIFFERENTIAL EQUATIONS;1995年02期

本文編號：2060077