【摘要】：第二基本定理在Nevanlinna值分布理論中占有很重要的地位,可以用它來解決復(fù)微分方程和差分方程中很多問題,甚至直接可以判斷方程的解是否存在和唯一性。故Nevanlinna理論的第二基本定理形式是非常重要。本學(xué)位論文內(nèi)容包括:第1章介紹本學(xué)位論文的研究背景和主要的工作;第2章介紹Nevanlinna理論中的基礎(chǔ)知識和本文中用到的相關(guān)知識;第3章介紹運用高等代數(shù)中的線性方程和矩陣的知識將單復(fù)變量到復(fù)射影空間中分擔(dān)超平面的差分形式下的第二基本定理的結(jié)果成功地推廣到單復(fù)變量到復(fù)射影空間中分擔(dān)超曲面的差分形式下的第二基本定理及其相關(guān)的結(jié)論;第4章介紹費馬型微分差分方程解的值分布的一些結(jié)果。
[Abstract]:The second fundamental theorem plays an important role in Nevanlinna's value distribution theory. It can be used to solve many problems in complex differential equation and difference equation, and even to judge the existence and uniqueness of the solution of the equation directly. Therefore, the form of the second fundamental theorem of Nevanlinna's theory is very important. The contents of this dissertation include: chapter 1 introduces the research background and main work of this thesis; the second chapter introduces the basic knowledge of Nevanlinna theory and the related knowledge used in this paper; In chapter 3, we introduce the results of the second fundamental theorem which applies the knowledge of linear equations and matrices in higher algebra to the difference form of sharing hyperplane in complex projective spaces. The results of this theorem are successfully extended to simple complex variables to complex projective forms. The second fundamental theorem in the difference form of shared hypersurfaces in space and its related conclusions; In chapter 4, some results of the value distribution of solutions of differential difference equations of Fermat type are introduced.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O174.52;O175.7

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相關(guān)期刊論文 前1條

1 WONG Pit-Mann;LAW Hiu-Fai;WONG Philip P.W.;;A Second Main Theorem on P~n for difference operator[J];Science in China(Series A:Mathematics);2009年12期

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本文編號：2437493