单位圆内二阶线性微分方程解的复振荡
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摘要
主要研究单位圆Δ内二阶线性微分方程f″+A(z)f′+B(z)f=F(z)解的[p,q]级,其中A(z),B(z)?0和F(z)?0是单位圆Δ内[p,q]级有限的亚纯函数,从而得出了一些复振荡结论。
In this paper,we investigate the [p,q]-order of solution of second-order linear differential equation f″+A(z)f′+B(z)f=F(z),where A(z),B(z)?0 and F(z)?0 are finite [p,q]-order meromorphic functions in the unit disc Δ,we obtain several theorems about the complex oscillation of solutions.
In this paper,we investigate the [p,q]-order of solution of second-order linear differential equation f″+A(z)f′+B(z)f=F(z),where A(z),B(z)?0 and F(z)?0 are finite [p,q]-order meromorphic functions in the unit disc Δ,we obtain several theorems about the complex oscillation of solutions.
引文
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[7] CAO T B,Yi H Y.The growth of solutions of linear differential equations with coefficients of iterated order in the unit disc[J].Journal of mathematical analysis and applications,2006,319(1):278-294.
[8] CAO T B.The growth,oscillation and fixed points of solutions of complex linear differential equations in the unit disc[J].Journal of mathematical analysis and applications,2009,352(2):739-748.
[9] CAO T B,Deng Z S.Solutions of non-homogeneous linear differential equations in the unit disc[J].Annales polonici mathematici,2010,97(1):51-61.
[10] LATREUCH Z,BELA?DI B.Linear differential equations with analytic coefficients of [p,q]-order in the unit disc[J].Sarajevo journal of mathematics,2013,9(21):71-84.
[11] TU J,XU H Y,ZHANG C Y.On the zeros of solutions of any order of any order of derivative of second orderlinear differential equations taking small functions[J].Electronic journal of qualitative theory of differential equations,2011,23:1-27.
[12] LATREUCH Z,BELA?DI B.Complex oscillation of solutions and their derivatives of non-homogenous linear differetial equations in the unit disc[J].International journal of analysis and applications,2013,2(2):111-123.
[13] BELA?DI B.Growth and oscillation theory of [p,q]-order analytic solutions of linear differential equations in the unit disc[J].Journal of mathematical analysis,2012,3(1):1-11.
[14] HU H,ZHENG X M.Growth of solutions of linear differential equations with analytic coefficients of [p,q]-order in the unit disc[J].Electronic journal of differential equations,2014,2014(204):1-12.
[2] 张广厚.整函数与亚纯函数理论—亏值.渐进值和奇异方向[M].北京:科学出版社,1986.
[3] LAINE I.Nevanlinna theory and complex differential equations[M].Berlin:Walter de Gruyter,1993.
[4] 杨乐.值分布论及其新研究[M].北京:科学出版社,1982.
[5] TSUJI M.Potential theory in modern function theory[M].New York:Chelsea,1975.
[6] HEITTOKANGAS J.On complex differential equations in the unit disc[J].Annales academi? scientiarum fennic? mathematica dissertationes,2000,122:1-54.
[7] CAO T B,Yi H Y.The growth of solutions of linear differential equations with coefficients of iterated order in the unit disc[J].Journal of mathematical analysis and applications,2006,319(1):278-294.
[8] CAO T B.The growth,oscillation and fixed points of solutions of complex linear differential equations in the unit disc[J].Journal of mathematical analysis and applications,2009,352(2):739-748.
[9] CAO T B,Deng Z S.Solutions of non-homogeneous linear differential equations in the unit disc[J].Annales polonici mathematici,2010,97(1):51-61.
[10] LATREUCH Z,BELA?DI B.Linear differential equations with analytic coefficients of [p,q]-order in the unit disc[J].Sarajevo journal of mathematics,2013,9(21):71-84.
[11] TU J,XU H Y,ZHANG C Y.On the zeros of solutions of any order of any order of derivative of second orderlinear differential equations taking small functions[J].Electronic journal of qualitative theory of differential equations,2011,23:1-27.
[12] LATREUCH Z,BELA?DI B.Complex oscillation of solutions and their derivatives of non-homogenous linear differetial equations in the unit disc[J].International journal of analysis and applications,2013,2(2):111-123.
[13] BELA?DI B.Growth and oscillation theory of [p,q]-order analytic solutions of linear differential equations in the unit disc[J].Journal of mathematical analysis,2012,3(1):1-11.
[14] HU H,ZHENG X M.Growth of solutions of linear differential equations with analytic coefficients of [p,q]-order in the unit disc[J].Electronic journal of differential equations,2014,2014(204):1-12.