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一类高阶线性微分方程解的增长性 被引量：1

On the growth of solutions of some higher order linear differential equations
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摘要 设A1(z)是方程f″+P(z)f=0的非零解,其中P(z)是n次多项式,Aj(z)≠0(j=2,3…,k-1)是整函数,A0(z)是一个超越整函数且满足ρ(Aj)<ρ(A0)≤12,j=2,3…,k-1,那么方程f(k)+Ak-1(z)f(k-1)+…+A1(z)f'+A0(z)f=0的每一个非零解都是无穷级。 Let A1 （z） be a solution off＇ ＋ P（ z）f = 0 , where P（z） is a polynomial with deg （p） = n and let A1（z）≠0（j=2,3…,k-1） be entire functions , A0 （z） be a transcendental entire function which 1 satisfiesp（A1）〈p（A0）≤1/2,j=2,3…,k-1 . Then every nontrivial solution of the equationf^（k）＋Ak-1（z）f（k-1）＋…＋A1（z）f＇＋A0（z）f=0 satisfiesp（f） =∞.
作者 张石梅 伍鹏程 胡光明
机构地区 贵州师范大学数学与计算机科学院
出处 《贵州师范大学学报（自然科学版）》 CAS 2013年第3期46-49,共4页 Journal of Guizhou Normal University：Natural Sciences
基金 贵州省科技基金资助项目(黔科合J字LKS[2012]12)
关键词 线性微分方程 整函数 增长级 linear differential equations entire function order of growth
分类号 O174 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Bank 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.
  • 2Belaidi 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.
  • 3Fuchs 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.
  • 4Gundersen G G . Estimates for the logarithmic derivative of meromorphic function , plus similar estimates [ J ]. J London Math Soe , 1988,37:88-104.
  • 5Gundersen G G. Finte order solution of second order line- ar differential equations [ J]. Trans Amer Math Soc, 1988, 305:415-429.
  • 6Hayman W K. Meromorphie Functions [ M ]. Oxford: Clarendon Press, 1964.
  • 7Hellerstein 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.
  • 8Hille E. Lectures on Ordinary Differential Equations [ M]. California, London, Don Mills, Ontario: Addison- Wesley Publiching Company, Reading, Massachusetts- Menlo Park, 1969.
  • 9伍鹏程.整函数的辐角分布及其拟素性[J].贵州大学学报（自然科学版）,1992,9(3):140-145. 被引量：1
  • 10吴秀碧,伍鹏程.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[J].数学物理学报（A辑）,2013,33(1):46-52. 被引量：6

二级参考文献16

  • 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.

共引文献5

同被引文献14

  • 1杨乐.值分布及其新研究[M].北京:中国科学出版社,1982.
  • 2HAYMAN W K. Meromorphic Functions [ M]. Ox-ford: Clarendon Press, 1964.
  • 3ROSSI J,WANG S P. The Radial Oscillation of Solu-tions to ODE’s in the Complex Domain[J]. Proc Edin-burgh Math Soc* 1996,39 :473-483.
  • 4WU S J. On the Location of Zeros of Solution of f +Af=0 Where is Entire[J]. Math Scand,1994,74 :293-312.
  • 5戴崇基,嵇善瑜.p级射线及其Borel方向分布间的关系[J].上海师范大学学报:自然科学版,1980,2: 16-24.
  • 6GUNDERSEN G G. Finte Order Solution of SecondLinear Differential Equations [J]. Trans Amer MathSoc,1988,305(1):415-429.
  • 7CHEN Z X,GAO S A. The Complex Oscillation The-ory of Certain Non-homogeneous Linear DifferentialEquations with Transcendental Entire Coefficients[J].J Math App,1993,179(2) :403-416.
  • 8GUNDERSEN G G. Estimates for the LogarithmicDerivative of a Meromorphic Function, Plus Simi-larEstimates[J], J London Math Soc, 1988, 37 ( 2 ) : 88-.
  • 9HILLE E. Lecture on Ordinary Differential Equations[M]. California,London,Don Mills, Ontario: Addison-Wesley Publishing Company, Reading, Massachusetts-Menlo Park, 1969.
  • 10戴崇基.关于整函数阶射线的个数[J].华东师范大学学报:自然科学版,1979:30-33.

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贵州师范大学学报（自然科学版）
2013年 第3期

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