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关于一类二阶微分方程解的增长性 被引量：1

ON THE GROWTH OF SOLUTIONS OF SOME SECOND-ORDER DIFFERENTIAL EQUATIONS
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摘要 本文研究一类二阶微分方程解的增长性,其中方程的系数是级为n的整函数.利用Nevanlinna值分布的基本理论和复振荡理论证明,得到当其系数满足一定条件时,这类方程的每个非零解有无穷级且超级为n,推广了Kwon[12]和陈宗煊[13,14]等人的结果. This paper investigates the growth of solutions of some second-order differential equations, where the coefficients of the equations are entire functions of order n. By using fundamental theorems of Nevanlinna＇s value distribution theory and the complex oscillation theory, we obtain that, when the coefficients satisfy some conditions, each non-zero solution of the above equation has infinite order and hyper-order n, which improve the results of Kwon [12] and Chen Zongxuan [13, 14].
作者 彭锋 陈裕先 陈宗煊
机构地区 华南师范大学数学科学学院 新余学院数学与计算机科学学院
出处 《数学杂志》 CSCD 北大核心 2013年第1期127-137,共11页 Journal of Mathematics
基金 江西省教育厅科技项目基金资助(GJJ11640)
关键词 微分方程 整函数 增长级 超级 differential equation entire function order of growth hyper-order
分类号 O174.5 [理学—基础数学]
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  • 1Hayman W. Meromorphic Function[M]. Oxford:Clarendon Press, 1964.
  • 2Gundersen G. Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates[J]. J London Math Soc , 1988,37(2) :88 - 104.
  • 3Markushevich A I. Theory of functions of a complex variable[ J]. Translated by Silverman R A. Englewood Cliffs: Prentice - Hall, 1965,(2).
  • 4Amemiya, I. & Ozawa, M., Non-existence of finite order solutions of w" + e-zw′ + Q(z)w = 0, Hokkaido Math. J., 10(1981), 1-17.
  • 5Chen Zongxuan & Yang Chungchun, Some further results on the zeros and growths of entire solutions of second order linear differential equations, Kodai Math. J., 22(1999), 273-285.
  • 6Chen Zongxuan, The growth of solutions of the differential equation f" + e-zf' + Q(z)f = 0 (in Chinese), Science in China, Series A, 31(2001), 775-784.
  • 7Frei, M., Uberdiesubnormalenlosungenderdifferentialgleichungw"+e-zw'+(konst.)w = 0, Comment.Math. Helv., 36(1962), 1-8.
  • 8Gundersen, G., On the question of whether f" + e-zf' + B(z)f = 0 can admit a solution f 0 of finite order, Proc, R.S.E., 102A(1986), 9-17.
  • 9Gundersen, G., Finite order solutions of second order linear differential equations, Trans. Amer. Math.Soc., 305(1988), 415-429.
  • 10Gundersen, G., Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc., 37:2(1988), 88-104.

共引文献64

同被引文献15

  • 1Hayman W K. Meromorphic functions [M]. Oxford: Clarendon Press, 1964.
  • 2Zhang G H. Theory of entire and meromorphic functions-deficient and asymptotic values and sin- gular directions [M]. Berlin: Springer-Verlag, 1993.
  • 3Tsuji M. Potential theory in modern function theory [M]. New York: Chelsea, 1975.
  • 4Laine I. Nevanlinna theory and complex differential equations [M]. New York: Walter de Gruyter, 1993.
  • 5Laine I. Complex differential equations [M]. Handbook of Differential Equations, Ordinary Differ- ential Equations, Vol. 4, Amsterdam: Elsevier, 2008.
  • 6Heittokangas J. On complex differential equations in the unit disc [D]. Ann. Acad. Sci. Fenn. Math. Diss., 2000, 122: 1-54.
  • 7Chen Z X, Shon K H. The growth of solutions of differential equations with coefficients of small growth in the disc [J]. J. Math. Anal. Appl., 2004, 297: 285-304.
  • 8Cao T B. The growth, oscillation and fixed points of solutions of complex linear differential equations in the unit disc [J]. J. Math. Anal. Appl., 2009, 352: 739-748.
  • 9Wu S J. On the growth of solutions of second order linear differential equations in an angle [J] Complex Var. Theory Appl., 1994, 24(3-4): 241-248.
  • 10Gol'dberg A A, Ostrovskii I V. Value distribution of meromorphic functions [M]. Trans. Math Monographs, Vol. 236, Providence, RI: American Math. Soc., 2008.

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数学杂志
2013年 第1期

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