本文選題：微分方程 + 亞純函數(shù)��； 參考：《江西師范大學(xué)》2015年碩士論文

【摘要】：本文主要研究高階線性微分方程解的復(fù)振蕩性質(zhì)及亞純函數(shù)分擔(dān)一個公共小函數(shù)的唯一性問題.全文共分四章.第一章,簡要介紹研究內(nèi)容的背景知識和相關(guān)預(yù)備理論知識,側(cè)重介紹Nevanl lnna理論中的一些基本結(jié)果,它們是研究微分方程復(fù)振蕩理論和亞純函數(shù)唯一性理論的重要工具.第二章,研究了一類整函數(shù)系數(shù)高階齊次線性微分方程解的零點分布.利用Ne vanlinna值分布理論,得到當系數(shù)Ak-1的增長性起主要支配作用時,方程f(κ)+Aκ-1f(κ-1)+…+Aof=0任意超越解的零點收斂指數(shù)為無窮.第三章,研究了亞純系數(shù)高階線性微分方程f(κ)+Aκ-1f(κ-1)+…+Aof=0解的增長性.證明了如果Ao(z)以∞為虧值,Aj(z)(0≤j≤k-1)滿足某些條件,則上述方程的每個非零亞純解都為無窮級,并得到非零亞純解的超級的下界估計.第四章,研究了亞純函數(shù)(或整函數(shù))關(guān)于微分多項式弱分擔(dān)一個多項式的唯一性問題,得到兩個亞純函數(shù)唯一性定理,推廣了Li和Yi.Chen和Zhang所得結(jié)裂.
[Abstract]:In this paper, we study the complex oscillatory properties of solutions of higher order linear differential equations and the uniqueness of meromorphic functions sharing a common small function. The full text is divided into four chapters. In the first chapter, we briefly introduce the background knowledge and the related presupposition theory of the research content, focusing on some basic results of Nevanl lnna theory, which are important tools for studying the complex oscillation theory of differential equations and the uniqueness theory of meromorphic functions. In chapter 2, the zero distribution of solutions for a class of high order homogeneous linear differential equations with whole function coefficients is studied. By using the distribution theory of ne vanlinna value, the equation f (魏) A 魏 -1f (魏 -1) is obtained when the growth of coefficient Ak-1 plays a dominant role. The zero convergence exponent of Aof=0 's arbitrary transcendental solution is infinite. In chapter 3, we study the meromorphic coefficient higher order linear differential equation f (魏) A 魏 -1 f (魏 -1). The growth of Aof=0 solution. It is proved that every nonzero meromorphic solution of the above equation is of infinite order if Aoz) satisfies some conditions by using 鈭，

本文編號：2009893