二阶线性微分方程解的增长性的新探索.pdf

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1、学校代码：10663学号:4201210000333贵贵贵州州州师师师范范范大大大学学学硕硕硕士士士学学学位位位论论论文文文二二二阶阶阶线线线性性性微微微分分分方方方程程程解解解的的的增增增长长长性性性的的的新新新探探探索索索Newexplorationofthegrowthoftwoorderlineardifferentialequations专业名称：基础数学专业代码：070101研究方向：函数论申请人姓名：张杰导师姓名：伍鹏程教授二零一五年四月目录摘摘摘要要要··········································

2、·················································1Abstract···························································································2引引引言言言与与与主主主要要要结结结果果果···················································································32二二二阶阶阶线线线性性性微微微分分分方方方程

3、程程解解解的的的增增增长长长性性性的的的新新新探探探索索索···········································6参参参考考考文文文献献献····························································································13致致致谢谢谢···························································································15

4、原原原创创创性性性声声声明明明·························································································161摘要内容摘要：本文主要是应用复分析的理论和方法来研究三种二阶线性微分方程解的增长性质,得到了如下三个结果：定理1设?(?)与?(?)是方程?′′+?(?)?=0的两个线性无关解，其中?(?)是n次多项式，且?(?)

5、解，其中?(?)是n次多项式，设?∈?且满足?1?(?,?2)=0，记?=?1−??2，则A没有有穷borel例外值。定理3设A,B为亚纯函数，?(∞,?)>0且?(?)>?(?)时，则方程?(?′′)+??(?′)+??(?)=0的每一个非零解都是无穷级。关关关键键键词词词:亚纯函数增长级零点聚直线亏值1AbstractInthispaper,wemainlyappliedthetheoryandmethodsofthecomplexanalysistostudythethreekindsofgrowthpropertiesofsecondorde

6、rlineardierentialequations.Firstly,Th1:Let?(?)and?(?)betwolinearlyindependentsolutionsof?′′+?(?)?=0,Where?(?)isapolynomial,and?(?)

7、polynomial,let?∈??1andfor?(?,?2)=0,let?=?1−??2,Then?(?)hasnoniteBorelexceptionalvalues.Inaddition,Th3:Let?(?)and?(?)beformeromorphicfunction,let?(∞,?)>0and?(?)>?(?),Theneverynonzerosolutionof?(?′′)+??(?′)+??(?)=0isofinniteorder.KeyWords:meromorphicfunctionorderofgrowthzeropol

8、ylineDeficientvalues2引引引言言言与与与主主主要要要结结结果果果1.1国国国内内内外外外