超越亚纯函数差分的值分布
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摘要
利用亚纯函数的Nevanlinna值分布理论,研究了超越亚纯函数差分的值分布问题,得到了2个超越亚纯函数的值分布结果,推广和改进了一些文献中的结论.
Based on the Nevanlinna theory of the value distribution of meromorphic functions difference,the value distribution problem of transcendental two meromorphic function difference was discussed,two new results were obtained,and some existing results were improved and generalized.
Based on the Nevanlinna theory of the value distribution of meromorphic functions difference,the value distribution problem of transcendental two meromorphic function difference was discussed,two new results were obtained,and some existing results were improved and generalized.
引文
[1]HAYMAN W K.Picardvalue of meromorphic function and their derivatives[J].Western Historical Quarterly,1959,70(1):9-42.
[2]HAYMAN W K.Research problems in function thery[M].London:Athlone Prees,1967.
[3]MUES E.Uber ein problem von Hayman[J].Mathematische Zeitschrift,1979,164(3):239-259.
[4]BERGWEILER W,Eremenko A.On the singularities of the inverse to a of meromorphic function of finite order[J].Revista Matematica Iberoamericana,1999,11(2):355-373.
[5]CHEN H H,FANG M L.On the value distribution of fnf′[J].Science in China,1995,38A:789-798.
[6]LIU K,QI X G.Meromorphic solutions of q-shifl difference equations[J].Annales Polonici Mathematici,2011,101(3):215-225.
[7]Halburd R G,Korhonen R J.Difference analogue of the lemma on the logarithmic derivative with applications to difference equations[J].Journal of Mathematical Analysis&Applications,2005,314(2):477-487.
[8]Chiang Y M,Feng S J.On the Nevanlinna characteristic of f(z+η)and difference equations in the complex plane[J].Ramanujan Journal,2008,16(1):105-129.
[9]张然然,陈宗煊.亚纯函数差分多项式的值分布[J].中国科学:数学,2012,42(11):1115-1130.ZHANG Ranran,CHEN Zongxuan.Value distribution of difference polynomials of meromorphic Functions[J].Sci Sin Math,2012,42(11):1115-1130.
[10]金瑾.关于亚纯函数φ(z)f(z)f(k)(z())nP[f]的值分布[J].应用数学,2013,26(3):499-505.JIN Jin.The value distribution of the meromorphic functionφ(z)fn(z)P[f][J].Mathematica Applicata,2013,26(3):499-505.
[11]金瑾.关于亚纯函数φ(z)fn(z)f(k)()z的值分布[J].纯粹数学与应用数学,2012,28(6):711-718.JIN Jin.The value distribution of the meromorphic functionφ(z)fn(z)f(k)(z)[J].Pure and Applied Mathematics,2012,28(6):711-718.
[12]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(自然科学版),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.
[13]金瑾.高阶复微分方程解的超级的角域分布[J].数学的实践与认识,2008,38(12):178-187.JIN Jin.The angular distribution of the solutions of higher order dif ferential Equation[J].Mathematics in Practice and Theory,2008,38(12):178-187.
[14]金瑾,武玲玲,樊艺.高阶非线性微分方程组的亚纯允许解[J].东北师范大学学报(自然科学版),2015,47(1):22-25.JIN Jin,WU Lingling,FAN Yi.Meromorphic admissible solution of systems of higher order non-linear complex differential eguations[J].Journal of Northeast Normal University(Natural Science Edition),2015,47(1):22-25.
[15]金瑾.单位圆内高阶齐次线性微分方程解与小函数的关系[J].应用数学学报,2014,37(4):754-764.JIN Jin.The retween solutions of higher order homogeneous linear differential equations and small functions in the unit dise[J].Acta Mathematicae Applicatae Sinica,2014,37(4):754-764.
[16]金瑾.一类高阶齐次线性微分方程的亚纯解与其小函数的复振荡[J].工程数学学报,2014,31(3):399-405.JIN Jin.On the complex oscillation of meromorphic solutions of a class of higher order homogeneous linear differential equations and functions of small growth[J].Chinese Journal of Engineering Mathematics,2014,31(3):399-405.
[17]金瑾,李泽清.一类高阶非线性微分方程组的亚纯允许解[J].应用数学,2014,27(2):292-298.JIN Jin,LI Zeqing.Meromorphic admissible solution of systems of higher order non-linear differential equations[J].Mathematica Applicata,2014,27(2):292-298.
[18]金瑾,李里.关于亚纯函数φ(z)f(z)M[f]的值分布[J].华中师范大学学报(自然科学版),2015,49(4):483-487.JIN Jin,LI Li.The value distribution of the meromorphic functionφ(z)f(z)M[f][J].Journal of Central China Normal University(Natural Sciences),2015,49(4):483-487.
[19]金瑾.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[J].Journal of Shanghai Jiaotong University,2013,47(7):1155-1159.
[20]王琼燕,叶亚盛.亚纯函数差分多项式的值分布和唯一性[J].数学年刊,2014,35A(6):675-684.WANG Qiongyan,YE Yasheng.Value distribution and uniqueness of difference polynomials of meromorphic function[J].Chinese Annals of Mathematics,2014,35A(6):675-684.
[2]HAYMAN W K.Research problems in function thery[M].London:Athlone Prees,1967.
[3]MUES E.Uber ein problem von Hayman[J].Mathematische Zeitschrift,1979,164(3):239-259.
[4]BERGWEILER W,Eremenko A.On the singularities of the inverse to a of meromorphic function of finite order[J].Revista Matematica Iberoamericana,1999,11(2):355-373.
[5]CHEN H H,FANG M L.On the value distribution of fnf′[J].Science in China,1995,38A:789-798.
[6]LIU K,QI X G.Meromorphic solutions of q-shifl difference equations[J].Annales Polonici Mathematici,2011,101(3):215-225.
[7]Halburd R G,Korhonen R J.Difference analogue of the lemma on the logarithmic derivative with applications to difference equations[J].Journal of Mathematical Analysis&Applications,2005,314(2):477-487.
[8]Chiang Y M,Feng S J.On the Nevanlinna characteristic of f(z+η)and difference equations in the complex plane[J].Ramanujan Journal,2008,16(1):105-129.
[9]张然然,陈宗煊.亚纯函数差分多项式的值分布[J].中国科学:数学,2012,42(11):1115-1130.ZHANG Ranran,CHEN Zongxuan.Value distribution of difference polynomials of meromorphic Functions[J].Sci Sin Math,2012,42(11):1115-1130.
[10]金瑾.关于亚纯函数φ(z)f(z)f(k)(z())nP[f]的值分布[J].应用数学,2013,26(3):499-505.JIN Jin.The value distribution of the meromorphic functionφ(z)fn(z)P[f][J].Mathematica Applicata,2013,26(3):499-505.
[11]金瑾.关于亚纯函数φ(z)fn(z)f(k)()z的值分布[J].纯粹数学与应用数学,2012,28(6):711-718.JIN Jin.The value distribution of the meromorphic functionφ(z)fn(z)f(k)(z)[J].Pure and Applied Mathematics,2012,28(6):711-718.
[12]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(自然科学版),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.
[13]金瑾.高阶复微分方程解的超级的角域分布[J].数学的实践与认识,2008,38(12):178-187.JIN Jin.The angular distribution of the solutions of higher order dif ferential Equation[J].Mathematics in Practice and Theory,2008,38(12):178-187.
[14]金瑾,武玲玲,樊艺.高阶非线性微分方程组的亚纯允许解[J].东北师范大学学报(自然科学版),2015,47(1):22-25.JIN Jin,WU Lingling,FAN Yi.Meromorphic admissible solution of systems of higher order non-linear complex differential eguations[J].Journal of Northeast Normal University(Natural Science Edition),2015,47(1):22-25.
[15]金瑾.单位圆内高阶齐次线性微分方程解与小函数的关系[J].应用数学学报,2014,37(4):754-764.JIN Jin.The retween solutions of higher order homogeneous linear differential equations and small functions in the unit dise[J].Acta Mathematicae Applicatae Sinica,2014,37(4):754-764.
[16]金瑾.一类高阶齐次线性微分方程的亚纯解与其小函数的复振荡[J].工程数学学报,2014,31(3):399-405.JIN Jin.On the complex oscillation of meromorphic solutions of a class of higher order homogeneous linear differential equations and functions of small growth[J].Chinese Journal of Engineering Mathematics,2014,31(3):399-405.
[17]金瑾,李泽清.一类高阶非线性微分方程组的亚纯允许解[J].应用数学,2014,27(2):292-298.JIN Jin,LI Zeqing.Meromorphic admissible solution of systems of higher order non-linear differential equations[J].Mathematica Applicata,2014,27(2):292-298.
[18]金瑾,李里.关于亚纯函数φ(z)f(z)M[f]的值分布[J].华中师范大学学报(自然科学版),2015,49(4):483-487.JIN Jin,LI Li.The value distribution of the meromorphic functionφ(z)f(z)M[f][J].Journal of Central China Normal University(Natural Sciences),2015,49(4):483-487.
[19]金瑾.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[J].Journal of Shanghai Jiaotong University,2013,47(7):1155-1159.
[20]王琼燕,叶亚盛.亚纯函数差分多项式的值分布和唯一性[J].数学年刊,2014,35A(6):675-684.WANG Qiongyan,YE Yasheng.Value distribution and uniqueness of difference polynomials of meromorphic function[J].Chinese Annals of Mathematics,2014,35A(6):675-684.