| 二阶线性微分方程复振荡的若干结果 |
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| 引用本文： | 袁文俊. 二阶线性微分方程复振荡的若干结果[J]. 数学学报, 1995, 38(1): 45-50. DOI: cnki:ISSN:05831431.0.1995-01-006 |
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| 作者姓名： | 袁文俊 |
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| 作者单位： | 伊犁师范学院数学系 |
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| 基金项目： | 新疆教委高校科研资助课题 |
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| 摘 要： | 本文给出了方程（１１）具有一个（或两个线性无关）解其零点收敛指数小于（或不小于）Ａ（ｚ）的增长级的必要条件（或充分条件）．我们得到了４个定理并且推广了Ｉ．Ｌａｉｎｅ的两个结果，我们还证明了如果Ａ（ｚ）是无穷级的整函数，则方程（１．１）的任两线性无关解或者无零点或者至少有一解其零点收敛指数为无穷．
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| 关 键 词： | 复振荡，收敛指数，增长级，解线性无关 |
| 收稿时间： | 1993-05-06 |
Some Complex Oscillation Results of Solutions of Second-Order Linear DifferentialEqtiations |
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| Yuan Wenjun. Some Complex Oscillation Results of Solutions of Second-Order Linear DifferentialEqtiations[J]. Acta Mathematica Sinica, 1995, 38(1): 45-50. DOI: cnki:ISSN:05831431.0.1995-01-006 |
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| Authors: | Yuan Wenjun |
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| Affiliation: | Yuan Wenjun(Department of Mathematics of Teachers Collape,Ili 835000, China) |
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| Abstract: | We give essential(or sufficient)conditions on A(z)that the equation y" A(z)y=0possess one(or two linearly independent)solution with the exponent of convergence of its zerosless(or no less)than the growth orderof A(z).We obtain four theorems and generalize tworesults of I. Laine. We also prove tliat if A(z)is an entire of infinite order,then any two linearlyindependent solutions of y" A(z)y=0 have no zeros unless the maximum value of the exponentsof convergence of their zeros is infinite. |
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| Keywords: | complex oscillation the exponent of convergence growth order linearly indepen-dent solutions |
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