一类高阶整函数系数微分方程解的增长级、下级与超级

Abstract

Abstract:

This paper investigates the properties of growth of solutions of a class of higher order linear differential equations with entire coefficients, obtains some precise estimates of the order and lower order of growth and the hyper-order of the solutions of equations f{(k)}+A_k-1(z)e^ak-1z,f ^(k-1)+… + A₀(z)e^a0zf =0 and f ^(k)+(A_k_-1}(z)e^ak-1z +D_k_-1(z)f ^(k-1)+…+(A₀(z)e^a0z+D₀(z)f =0 when the arguments of a_j,0≤ j ≤ k-1, are not all equal.

Key words: Differential equation, Entire function, Order and lower order of growth, Hyper-order

CLC Number:

30D35

Cite this article

CHEN Yu. The Order, and |Lower Order of Growth, and the Hyper-order of a Class of Higher Order Linear Differential Equations with Entire[J].Acta mathematica scientia,Series A, 2010, 30(4): 1030-1041.

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References

[1] 杨乐. 值分布及其新研究.北京:科学出版社,1982

[2] 何育赞, 萧修治. 代数体函数与常微分方程. 北京:科学出版社, 1998

[3] Frei M. Uber die subnormalen losungen der differentialgleichung \omega''+{\rm e}^{-z}\omega'+{\rm (konst.)}\omega=0. Comment Math Helv, 1962, 36: 1--8

[4] Ozawa M. On a solution of \omega''+{\rm e}^{-z}\omega'+(az+b)\omega=0. Kodai Math J,1980, 3: 295--309

[5] Amemiya I, Ozawa M. Non-existence of finite order solutions of \omega''+{\rm e}^{-z}\omega'+Q(z)\omega=0. Hokkaido Math J,1981, 10: 1--17

[6] Gundersen G. On the question of whether f''+{\rm e}^{-z}f'+B(z)f=0 can admit a solution f \not\equiv 0 of finite order. Proc R S E, 1986, 102A: 9--17

[7] Langley J K. On complex oscillation and a problem of Ozawa. Kodai Math J, 1986, 9: 430--439

[8] 陈宗煊.关于微分方程f''+{\rm e}^{-z}f'+B(z)f=0的增长性.中国科学(A辑), 2001, 31(9): 775--784

[9] 李纯红, 黄小军. 一类高阶线性微分方程解的增长性.数学物理学报, 2003, 23A(5): 613--618

[10] Chen Zongxuan, Shon Kwangho. On the growth of solutions of a class of higher order differential equations. Acta Mathematica Scientia, 2004, 24B(1): 52--60

[11] Chen Zongxuan. On the hyper order of solutions of higher order differential equations. Chin Ann Math, 2003, 24B(4): 501--508

[12] Gundersen G. Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. J London Math Soc, 1988, 37(2): 88--104

[13] 涂金, 陈宗煊. 一类高阶微分方程解的增长性.数学物理学报, 2008, 28A(4): 670--678

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The Order, and |Lower Order of Growth, and the Hyper-order of a Class of Higher Order Linear Differential Equations with Entire

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