| 方程f″+Af'+Bf=0的解在角域内的增长性及Borel方向 |
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| 引用本文： | 易才凤,刘旭强.方程f″+Af'+Bf=0的解在角域内的增长性及Borel方向[J].江西师范大学学报(自然科学版),2013,0(1):1-5. |
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| 作者姓名： | 易才凤 刘旭强 |
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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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| 基金项目： | 国家自然科学基金(11171170)资助项目 |
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| 摘 要： | 运用角域内值分布的理论和方法,研究了整系数2阶线性微分方程f”+Af’+Bf=0的解在角域内的增长性和Borel方向.在给定条件下,证明了方程的每一非零解在含有B的λ(λ＞0)级Borel方向的任意角域内的增长级均为无穷,且B的λ级Borel方向与解的无穷级Borel方向一致.
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| 关 键 词： | 微分方程 解 角域 Borel方向 无穷级 |
The Growth and Borel Direction of Solutions for Differential Equation f" + Af' + Bf =0 in Angular Domains |
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| YI Cai-feng,LIU Xu-qiang.The Growth and Borel Direction of Solutions for Differential Equation f" + Af' + Bf =0 in Angular Domains[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2013,0(1):1-5. |
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| Authors: | YI Cai-feng LIU Xu-qiang |
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| Institution: | (College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China) |
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| Abstract: | The growth and Borel direction of solutions in angular domains for differential equation f ″+Af '+Bf=0 is investigated where A(z) and B(z) are entire functions,by using the fundamental theory and method of value distribution in angular domain.Under some conditions,it is proved that every solution f0 of the equation is of infinite order in any angular domain which has λ order Borel direction of B(z),and the ∞order Borel direction of the solution is unanimous with the λ order Borel direction of B(z). |
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| Keywords: | differential equations solutions angular domain Borel direction infinite order |
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