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

【摘要】：本文運(yùn)用Nevanlinna值分布理論分別在復(fù)平面上和單位圓內(nèi)研究了幾類復(fù)線性微分方程亞純解的增長(zhǎng)性和值分布.同時(shí),還研究了一類q-平移差分-微分多項(xiàng)式的值分布.所得結(jié)果是對(duì)前人已有結(jié)果的推廣和改進(jìn).全文分為四章.第一章,扼要介紹了復(fù)線性微分方程值分布理論和復(fù)差分與差分方程理論的主要發(fā)展線索,同時(shí)介紹了本文主要內(nèi)容和一些基本定義.第二章,在復(fù)平面上研究了一類具有Lacunary缺項(xiàng)級(jí)數(shù)系數(shù)的高階齊次和非齊次線性微分方程亞純解的[p,q]級(jí)和[p,q]下級(jí)及解取小函數(shù)值點(diǎn)的[p,q]收斂指數(shù)和[p,q]下收斂指數(shù).第三章,在單位圓內(nèi)研究了系數(shù)為亞純函數(shù)的齊次和非齊次線性微分方程亞純解的微分多項(xiàng)式取小函數(shù)值點(diǎn)的迭代收斂指數(shù)和迭代下收斂指數(shù).第四章,研究了一類正有窮級(jí)整函數(shù)的q-平移差分-微分多項(xiàng)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(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
【分類號(hào)】：O174.52

【參考文獻(xiàn)】

相關(guān)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

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