一类高阶微分方程亚纯解取小函数的收敛指数
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摘要
研究了亚纯函数系数的高阶线性微分方程亚纯解取小函数的点的收敛指数问题,获得了线性微分方程亚纯解取小函数的点的收敛指数的精确估计.
In this paper,the problems of convergence between the zeros of the solution of higher order linear differential equations with meromorphic coefficients and small order of growth function were studied,and some precise estimates between the meromorphic solution of linear differential equations and small order of growth function were obtained.
In this paper,the problems of convergence between the zeros of the solution of higher order linear differential equations with meromorphic coefficients and small order of growth function were studied,and some precise estimates between the meromorphic solution of linear differential equations and small order of growth function were obtained.
引文
[1]BANK S,LAINE I.On the oscillation theory of f″+Af=0 where a is entire[J].Transactions of the American Mathematical Society,1982,273(1):351-363.
[2]GAO Shian.On the complex oscillation of solutions of nonhomogeneous linear differential equations with Polyno-Mial coefficients[J].Comment Mathematica Universitatis Sancti Parli,1989,38(2):11-20.
[3]KI-HO kwon.Nonexistence of finite order solutions of certain second order linear differential equations[J].Kodai Mathematical Journal,1996,19(1):378-387.
[4]GUNDERSEN G.Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates[J].Journal London Mathematica Society,1988,37(2):88-104.
[5]梁建军,刘名生.高阶亚纯系数非齐次线性微分方程的复振荡[J].纯粹数学与应用数学,2006,22(4):464-470.LIANG Jianjun,LIU Mingsheng.The complex oscillation of higher order nonhomogeneous linear differential equations with meromorphic coefficients[J].Pure and Applied Mathematics,2006,22(4):464-470.
[6]陈宗煊.关于高阶线性微分方程亚纯解的增长率[J].数学学报,1999,42(3):551-558.CHEN Zongxuan.On the rate of growth of meromorphic solutions of higher order linear differential equations[J].Acta Mathematica Sinica,1999,42(3):551-558.
[7]陈宗煊.微分方程f″+A1(z)eazf′+A0(z)ebzf=0的解的增长性[J].中国科学:A辑,2001,31(9):775-784.CHEN Zongxuan.The growth of solutions differential equations f″+A1(z)eazf′+A0(z)ebzf=0[J].Science China Mathematics,2001,31(9):775-784.
[8]陈宗煊,孙光镐.一类二阶微分方程的解和小函数的关系[J].数学年刊:A辑,2006,27(4):431-442.CHEN Zongxuan,SHUN Guanggao.The relation between solutions of a class of second order differential equation whth functions of small growth[J].Chinese Annals of Mathematics,2006,27A(4):431-442.
[9]CHEN Zongxuan.Zeros of meomorphic solutions of higher order linear differential equations[J].Analysis,1994,14:425-438.
[10]金瑾.关于高阶线性微分方程解与其小函数的增长性[J].上海交通大学学报,2013,47(7):1155-1159.JIN Jin.Growth of solutions of higher order linear differential equations and its small functions[J].Journal of Shanghai Jiaotong University,2013,47(7):1155-1159.
[12]金瑾.一类高阶齐次线性微分方程解的增长性[J].华中师范大学学报,2013,47(1):4-7.JIN Jin.The growth of the solutions of some higher order homogeneous linear differential equations[J].Journal of Huazhong Normal University Natural sciences,2013,47(1):4-7.
[13]金瑾.关于一类高阶齐次线性微分方程解的增长性[J].中山大学报,2013,52(1):51-55.JIN Jin.On the growth of solutions of higher order homogeneous linear differential equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2013,52(1):51-55.
[14]金瑾.高阶微分方程解与其小函数的关系[J].高校应用数学学报,2013,28(1):43-51.JIN Jin.Relations between solutions of a class of higher order homogeneous differential equations with functions of small growth[J].Applied Mathematics a Journal of Chinese Universities,2013,28(1):43-51.
[15]金瑾.关于亚纯函数φ(z)f(z)(fk)((z)n)P[f]的值分布[J].应用数学,2013,26(3):499-505.JIN Jin.The value distribution of the meromorphic function(k)φ(z)f(z)(f(z)n)P[f][J].Mathematica Applicata,2013,26(3):499-505.
[16]BARSEGIAN G.On a method of study of algebra is differential equations[J].Bull Hong Kong Mathematica Society,1998,2(1):159-164.
[17]BERGWEILER W.On a theorem of Gol’dberg concerning meromorphic solutions of algebraic differential equations[J].Complex Variables,1998,37(1):117-148.
[18]KINNUNEN L.Linear differential equations with solutions of finite order[J].Southeast Asian Bull Mathematica,1998,22(4):385-405.
[19]BELAIDIR Hamanik.Order and hyper-order of entire solutions of linear differential equations with entire coefficients[J].Electronic Journal Differ Equations,2003,8(13):1-2.
[20]LAINE I,RIEPPO J.Differential polynomials generated by linear differential equations[J].Complex Variables,2004,49:897-911.
[21]BANK S,LAINE I.On the zeros of meromorphic solutions of second order linear differential equations[J].Comment Mathematica Helv,1983,58(3):656-677.
[22]BANK S,LANGLEY J.On the oscillation of solutions of certain linear differential equations in the complex domain[J].Proceedings of Edinburgh Mathematical Society,1987,30(1):455-469.
[23]BANK S,LANGLEY J.Oscillation theory for higher order linear differential equations with entire confficients[J].Complex Variables,1991,16(1):163-175.
[24]LANGLEY J.Some oscillation theorems for higher order linear differential equations with coefficient of small growth[J].Results Mathematica,1991,20(2):517-529.
[2]GAO Shian.On the complex oscillation of solutions of nonhomogeneous linear differential equations with Polyno-Mial coefficients[J].Comment Mathematica Universitatis Sancti Parli,1989,38(2):11-20.
[3]KI-HO kwon.Nonexistence of finite order solutions of certain second order linear differential equations[J].Kodai Mathematical Journal,1996,19(1):378-387.
[4]GUNDERSEN G.Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates[J].Journal London Mathematica Society,1988,37(2):88-104.
[5]梁建军,刘名生.高阶亚纯系数非齐次线性微分方程的复振荡[J].纯粹数学与应用数学,2006,22(4):464-470.LIANG Jianjun,LIU Mingsheng.The complex oscillation of higher order nonhomogeneous linear differential equations with meromorphic coefficients[J].Pure and Applied Mathematics,2006,22(4):464-470.
[6]陈宗煊.关于高阶线性微分方程亚纯解的增长率[J].数学学报,1999,42(3):551-558.CHEN Zongxuan.On the rate of growth of meromorphic solutions of higher order linear differential equations[J].Acta Mathematica Sinica,1999,42(3):551-558.
[7]陈宗煊.微分方程f″+A1(z)eazf′+A0(z)ebzf=0的解的增长性[J].中国科学:A辑,2001,31(9):775-784.CHEN Zongxuan.The growth of solutions differential equations f″+A1(z)eazf′+A0(z)ebzf=0[J].Science China Mathematics,2001,31(9):775-784.
[8]陈宗煊,孙光镐.一类二阶微分方程的解和小函数的关系[J].数学年刊:A辑,2006,27(4):431-442.CHEN Zongxuan,SHUN Guanggao.The relation between solutions of a class of second order differential equation whth functions of small growth[J].Chinese Annals of Mathematics,2006,27A(4):431-442.
[9]CHEN Zongxuan.Zeros of meomorphic solutions of higher order linear differential equations[J].Analysis,1994,14:425-438.
[10]金瑾.关于高阶线性微分方程解与其小函数的增长性[J].上海交通大学学报,2013,47(7):1155-1159.JIN Jin.Growth of solutions of higher order linear differential equations and its small functions[J].Journal of Shanghai Jiaotong University,2013,47(7):1155-1159.
[12]金瑾.一类高阶齐次线性微分方程解的增长性[J].华中师范大学学报,2013,47(1):4-7.JIN Jin.The growth of the solutions of some higher order homogeneous linear differential equations[J].Journal of Huazhong Normal University Natural sciences,2013,47(1):4-7.
[13]金瑾.关于一类高阶齐次线性微分方程解的增长性[J].中山大学报,2013,52(1):51-55.JIN Jin.On the growth of solutions of higher order homogeneous linear differential equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2013,52(1):51-55.
[14]金瑾.高阶微分方程解与其小函数的关系[J].高校应用数学学报,2013,28(1):43-51.JIN Jin.Relations between solutions of a class of higher order homogeneous differential equations with functions of small growth[J].Applied Mathematics a Journal of Chinese Universities,2013,28(1):43-51.
[15]金瑾.关于亚纯函数φ(z)f(z)(fk)((z)n)P[f]的值分布[J].应用数学,2013,26(3):499-505.JIN Jin.The value distribution of the meromorphic function(k)φ(z)f(z)(f(z)n)P[f][J].Mathematica Applicata,2013,26(3):499-505.
[16]BARSEGIAN G.On a method of study of algebra is differential equations[J].Bull Hong Kong Mathematica Society,1998,2(1):159-164.
[17]BERGWEILER W.On a theorem of Gol’dberg concerning meromorphic solutions of algebraic differential equations[J].Complex Variables,1998,37(1):117-148.
[18]KINNUNEN L.Linear differential equations with solutions of finite order[J].Southeast Asian Bull Mathematica,1998,22(4):385-405.
[19]BELAIDIR Hamanik.Order and hyper-order of entire solutions of linear differential equations with entire coefficients[J].Electronic Journal Differ Equations,2003,8(13):1-2.
[20]LAINE I,RIEPPO J.Differential polynomials generated by linear differential equations[J].Complex Variables,2004,49:897-911.
[21]BANK S,LAINE I.On the zeros of meromorphic solutions of second order linear differential equations[J].Comment Mathematica Helv,1983,58(3):656-677.
[22]BANK S,LANGLEY J.On the oscillation of solutions of certain linear differential equations in the complex domain[J].Proceedings of Edinburgh Mathematical Society,1987,30(1):455-469.
[23]BANK S,LANGLEY J.Oscillation theory for higher order linear differential equations with entire confficients[J].Complex Variables,1991,16(1):163-175.
[24]LANGLEY J.Some oscillation theorems for higher order linear differential equations with coefficient of small growth[J].Results Mathematica,1991,20(2):517-529.