角域上高阶复线性微分方程解的[p,q]级
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摘要
利用Nevanlinna理论和共形变换的性质研究了角域上高阶复线性微分方程解的增长性问题,得到了复微分方程解在角域上[p,q]级增长的一些估计.
We study the growth problem of solutions of higher order complex Unear differential equations in an angular domain of the complex plane by using the Nevanlinna theory and the properties of conformal transformation.Some estimations of[p,q]-order of solutions of complex linear differential equations in an angular domain are obtained.
We study the growth problem of solutions of higher order complex Unear differential equations in an angular domain of the complex plane by using the Nevanlinna theory and the properties of conformal transformation.Some estimations of[p,q]-order of solutions of complex linear differential equations in an angular domain are obtained.
引文
[1]Pommerenke Chr.On the mean growth of the solutions of complex linear differential equations in the disc[J].Complex Var Ell Equa,1982,1(1):23-38.
[2]Heittokangas J.On complex differential equations in the unit disc[D].Ann Acad Sci Fenn Math Diss,2000,122:1-54.
[3]Bela(i|¨)di B.Growth of solutions to linear equations with analytic coefficients of[p,g]-order in the unit disc[J].Electron J Differential Equa,2011,156:1-11.
[4]Bela(i|¨)di B.On the[p,q]-order of analytic solutions of linear differential equations in the unit disc[J].Novi Sad J Math,2012,42(1):117-129.
[5]Cao Tingbin.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.
[6]Cao Tingbin,Yi Hongxun.The growth of solutions of complex differential equations in the unit disc[J].J Math Anal Appl,2006,319:278-294.
[7]Chen Zongxuan,Shon Kwangho.The growth of solutions of differential equations with coefficients of small growth in the disc[J].J Math Anal Appl,2004,297:285-304.
[8]Chen Zongxuan.The properties of solutions of a class of differential equations in the unit disc[J],J Jiangxi Norm Univer,2002,26(3):189-190.(In Chinese)
[9]Heittokangas J,Korhonen R,RattyaJ.Fast growing solutions of linear differential equations in the unit disc[J].Results Math,2006,49:265-278.
[10]Heittokangas J,Korhonen R,RattyaJ.Growth estimates for solutions of linear differential equations[J].Ann Acad Sci Fenn Math,2009,29(1):233-246.
[11]Heittokangas J,Korhonen R,RattyaJ.Linear differential equations with coefficients in weighted Bergman and Hardy space[J].Trans Amer Math Soc,2008,360:1035-1055.
[12]Long Jianren.Growth of solutions of higher order complex linear differential equations in an angular domain of unit disc[J].J Math Study,2015,48(3):306-314.
[13]Tu J,Huang H X.Complex oscillation of linear differential equations with analytic coefficients of[p,q]-order in the unit disc[J].Comput Methods Funct Theory,2015,15(2):225-246.
[14]Hayman W K.Meromorphic Functions[M].Oxford:Clarendon Press,1964.
[15]Tsuji M.Potential Theory in Modern Function Theory[M].New York:Chelsea,1975,reprint of the1959 edition.
[16]Zhang G H.Theory of Entire and Meromorphic Functions-Deficient and Asymptotic values and Singular Directions[M].Berlin:Springer-Verlag,1993.
[17]Laine I.Nevanlinna Theory and Complex Differential Equations[M].New York:Walter de Gruyter,1993.
[18]Laine I.Complex Differential Equations,in:Handbook of Differential Equations,Ordinary Differential Equations[M].vol.4,Elsevier,Amsterdam,2008.
[19]Wu Shengjian.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.
[20]Gol'dberg A A,Ostrovskii I V.Value Distribution of Meromorphic Functions[M].Translations of Mathematical Monographs,vol.236,American Mathematical Society,Providence,RI,2008.
[21]Xu Junfeng,Yi Hongxun.Solutions of higher order linear differential equations in an angle[J].Appl Math Letter,2009,22(4):484-489.
[22]Wu Nan.Growth of solutions to linear complex differential equations in an angular region[J].Electron J Differential Equa,2013,2013(183):1-8.
[23]Long Jianren.Growth of solutions of higher order complex Unear differential equations in an angular domain[J].J Math(Wuhan),2015,35(6):1533-1540.(In Chinese)
[24]Edrei A.Meromorphic functions with three radially distributed values[J].Trans Amer Math Soc,1955,78:276-293.
[2]Heittokangas J.On complex differential equations in the unit disc[D].Ann Acad Sci Fenn Math Diss,2000,122:1-54.
[3]Bela(i|¨)di B.Growth of solutions to linear equations with analytic coefficients of[p,g]-order in the unit disc[J].Electron J Differential Equa,2011,156:1-11.
[4]Bela(i|¨)di B.On the[p,q]-order of analytic solutions of linear differential equations in the unit disc[J].Novi Sad J Math,2012,42(1):117-129.
[5]Cao Tingbin.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.
[6]Cao Tingbin,Yi Hongxun.The growth of solutions of complex differential equations in the unit disc[J].J Math Anal Appl,2006,319:278-294.
[7]Chen Zongxuan,Shon Kwangho.The growth of solutions of differential equations with coefficients of small growth in the disc[J].J Math Anal Appl,2004,297:285-304.
[8]Chen Zongxuan.The properties of solutions of a class of differential equations in the unit disc[J],J Jiangxi Norm Univer,2002,26(3):189-190.(In Chinese)
[9]Heittokangas J,Korhonen R,RattyaJ.Fast growing solutions of linear differential equations in the unit disc[J].Results Math,2006,49:265-278.
[10]Heittokangas J,Korhonen R,RattyaJ.Growth estimates for solutions of linear differential equations[J].Ann Acad Sci Fenn Math,2009,29(1):233-246.
[11]Heittokangas J,Korhonen R,RattyaJ.Linear differential equations with coefficients in weighted Bergman and Hardy space[J].Trans Amer Math Soc,2008,360:1035-1055.
[12]Long Jianren.Growth of solutions of higher order complex linear differential equations in an angular domain of unit disc[J].J Math Study,2015,48(3):306-314.
[13]Tu J,Huang H X.Complex oscillation of linear differential equations with analytic coefficients of[p,q]-order in the unit disc[J].Comput Methods Funct Theory,2015,15(2):225-246.
[14]Hayman W K.Meromorphic Functions[M].Oxford:Clarendon Press,1964.
[15]Tsuji M.Potential Theory in Modern Function Theory[M].New York:Chelsea,1975,reprint of the1959 edition.
[16]Zhang G H.Theory of Entire and Meromorphic Functions-Deficient and Asymptotic values and Singular Directions[M].Berlin:Springer-Verlag,1993.
[17]Laine I.Nevanlinna Theory and Complex Differential Equations[M].New York:Walter de Gruyter,1993.
[18]Laine I.Complex Differential Equations,in:Handbook of Differential Equations,Ordinary Differential Equations[M].vol.4,Elsevier,Amsterdam,2008.
[19]Wu Shengjian.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.
[20]Gol'dberg A A,Ostrovskii I V.Value Distribution of Meromorphic Functions[M].Translations of Mathematical Monographs,vol.236,American Mathematical Society,Providence,RI,2008.
[21]Xu Junfeng,Yi Hongxun.Solutions of higher order linear differential equations in an angle[J].Appl Math Letter,2009,22(4):484-489.
[22]Wu Nan.Growth of solutions to linear complex differential equations in an angular region[J].Electron J Differential Equa,2013,2013(183):1-8.
[23]Long Jianren.Growth of solutions of higher order complex Unear differential equations in an angular domain[J].J Math(Wuhan),2015,35(6):1533-1540.(In Chinese)
[24]Edrei A.Meromorphic functions with three radially distributed values[J].Trans Amer Math Soc,1955,78:276-293.