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关于方程f″+Af′+Bf=0解的增长性,其中系数A是一个二阶线性微分方程的解 被引量：6

On the Growth of Solutions of f″+ Af′+ Bf=0,Where A is a Solution of a Second Order Linear Differential Equation
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摘要 设A(z)是方程f″+P(z)f=0的非零解,其中P(z)是n次多项式,B(z)是一个超越整函数且满足ρ(B)≤1/2.那么方程f″+Af′+Bf=0的每一个非零解都是无穷级.并且方程f″+A(z)f=0两个线性无关解乘积的零点序列收敛指数为无穷. Let A（z） be a nontrivial solution of f＂ ＋ P（z）f = 0, where P（z） is a polynomial and let B（z） be a transcendental entire function of order p≤1/2. Then every nontrivial solution of f＂ ＋ A（z）f′ ＋ B（z）f = 0 is of infinite order. Moreover, the exponent of convergence of zero-sequence of the product of two linearly independent solutions of f″ ＋ A（z）f = 0 is of infinite.
作者 吴秀碧 伍鹏程
机构地区 贵州大学 贵州师范大学
出处 《数学物理学报（A辑）》 CSCD 北大核心 2013年第1期46-52,共7页 Acta Mathematica Scientia
基金 国家自然科学基金(11171080) 贵州省科学技术基金(黔科合J字LKS[2010]07号)资助
关键词 增长级 线性微分方程 整函数 零点收敛指数 Order Linear differential equations Entire function Exponent of convergence ofzero-sequence.
分类号 O174.5 [理学—基础数学] O174.52 [理学—基础数学]
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参考文献15

  • 1Bank S B. A note on the zeros of solutions of w1 + P(z)w = 0 where P is a polynomial. Appl Anal, 1987, 25:29-41.
  • 2Bank S B, Laine I. On the oscillation theory of f Af = 0 where A is entire. Trans Amer Math Soc, 1982, 273:351-363.
  • 3Bank S B, Laine I, Langley J. On the frequency of zeros of solutions of secoond order linear differential equations. Results Math, 1986, 10:8- 24.
  • 4Fuchs W H J. Topics in Nevanlinna Theory. Proceedings of the NRL Conference on Classical Function Theory. Washington, DC: Naval Research Laboratory, 1970:1-32.
  • 5Guncersen G G. On the real zeros of solutions of f + A(z)f = 0 where A(z) is entire. Ann Acad Sci Fenn Math, 1986, 11:275-294.
  • 6Gundersen G G. Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J London Math Soc, 1988, 37:88- 104.
  • 7Gundersen G G. Finite order solution of second order linear differential equations. Trans Amer Math Soc, 1988, 305:415-429.
  • 8Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964 Hellerstein S, Rossi J. On the distribution of zeros of solutions of second-order differential equations. Complex Variables Theory Appl, 1989, 13:99-109.
  • 9Hellerstein S, Miles J, Rossi J. On the growth of solutions of certain linear differential equations. Ann Acad Sci Fenn (Ser A I Math), 1992, 17:343-365.
  • 10Hille E. Lectures on Ordinary Differntial Equations. California, London, Don Mills, Ontario: Addison- Wesley Publiching Company, Reading, Massachusetts-Menlo Park, 1969.

同被引文献51

  • 1杨乐.值分布及其新研究[M].北京:中国科学出版社,1982.
  • 2Bank S B, Laine I, Langley J. On the frequency of zeros of solutions of second order linear differential equations. Results Math, 1986,10:8-12.
  • 3Belaidi B. and Hamani K. Order and hyper-order of en- tire solutions of linear differential equations with coeffi- cients[J]. Electronic J Differ Equations, 2003 ( 17 ) : 1- 12.
  • 4Fuchs W H J. Topics in Nevanlinna Theory [ C ]. Proceedings of the NRL Conference on Classical Function Theory. Washington : DC : Naval Research Laboratory, 1970 : 1-32.
  • 5Gundersen G G . Estimates for the logarithmic derivative of meromorphic function , plus similar estimates [ J ]. J London Math Soe , 1988,37:88-104.
  • 6Gundersen G G. Finte order solution of second order line- ar differential equations [ J]. Trans Amer Math Soc, 1988, 305:415-429.
  • 7Hayman W K. Meromorphie Functions [ M ]. Oxford: Clarendon Press, 1964.
  • 8Hellerstein S, Miles J, Rossi J. On the growth of solu- tions of certain linear differential equations [ J ]. Ann Aead Sci Fenn( Ser A I Math), 1992,17:99-109.
  • 9Hille E. Lectures on Ordinary Differential Equations [ M]. California, London, Don Mills, Ontario: Addison- Wesley Publiching Company, Reading, Massachusetts- Menlo Park, 1969.
  • 10Yang Lo. Value Distribution Theory [ M ]. ( Translated and Revised from the 1982 Chinese Original). Berlin: Springer-Verlag. Beijing: Science Press, 1993.

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二级引证文献8

数学物理学报（A辑）
2013年 第1期

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