| 一类2阶线性微分方程解的增长性 |
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| 引用本文： | 涂鸿强,刘慧芳.一类2阶线性微分方程解的增长性[J].江西师范大学学报(自然科学版),2017,0(2):184-188. |
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| 作者姓名： | 涂鸿强 刘慧芳 |
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| 作者单位： | 江西师范大学数学与信息科学学院,江西 南昌 330022 |
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| 摘 要： | 研究2阶微分方程f ″+A1(z)f ’+A0(z)f=0解的增长性.假设A1(z)=h1eQ1(z)+h2eQ2(z),其中Qj(j=1,2)为n(n≥1)次多项式,hj(j=1,2)为级小于n的整函数,A0为满足下级μ(A0)≠n的超越整函数或A0为满足Denjoy猜想极值情况的整函数,得到上述方程的每个非零解都具有无穷级,同时对解的超级进行了估计.
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| 关 键 词： | 微分方程 整函数 Denjoy猜想 增长级 |
On Growth of Solutions of Some Second Order Linear Differential Equations |
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| TU Hongqiang,LIU Huifang.On Growth of Solutions of Some Second Order Linear Differential Equations[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2017,0(2):184-188. |
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| Authors: | TU Hongqiang LIU Huifang |
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| Institution: | College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China |
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| Abstract: | The growth of solutions of second order linear differential equations f ″+A1(z)f ’+A0(z)f=0 is investigated.Let A1(z)=h1eQ1(z)+h2eQ2(z),where Qj(z)(j=1,2) are polynomials with degree n(n≥1),hj(j=1,2) are entire functions with order less than n,and let A0 be a transcendental entire function with lower order μ(A0)≠n or A0 or a function extremal for Denjoy’s conjecture,then every nontrivial solution of such equations is of infinite order.Some estimates on hyper-order of its solutions are also obtained. |
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| Keywords: | differential equation entire function Denjoy’s conjecture order of growth |
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