二阶线性微分方程解与不动点的关系
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摘要
使用Nevanlinna值分布的基本理论和方法,研究了几类二阶线性微分方程解及解的导数与其不动点之间的关系,得到了方程解及其导数的不动点的不同点收敛指数为无穷和二级收敛指数等于解的超级的精确结果.
It was investigated that the relations between solutions of second order linear differential equations and their derivatives with fixed point by by using the theory and the method of Nevanlinna value distribution.The precision result was obtained that convergence exponents of various points of equation solutions and their derivatives fetch the fixed point is infinite and the second order convergence exponents with the hyper order of solution is equal.
It was investigated that the relations between solutions of second order linear differential equations and their derivatives with fixed point by by using the theory and the method of Nevanlinna value distribution.The precision result was obtained that convergence exponents of various points of equation solutions and their derivatives fetch the fixed point is infinite and the second order convergence exponents with the hyper order of solution is equal.
引文
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[10]安蕾,肖丽鹏.一类2阶微分方程的解和小函数的关系[J].江西师范大学学报:自然科学版,2013,37(3):233-235.
[11]袁蓉,刘慧芳.一类二阶非齐次线性微分方程解的复振荡[J].高校应用数学学报:自然科学版,2017,32(4):431-436.
[12]Chen Z X,Shon K H.On the growth of solutions of a class of higher order differential equations[J].Acta Math Sci,2004,24(1):52-60.
[13]Cheng T.The growth of a class of linear differential equation[J].Journal of Fudan University,2006,45(10):610-617.
[14]闵小花,张红霞,易才凤.2阶微分方程的解和小函数的关系[J].江西师范大学学报:自然科学版,2014,38(6):551-556.
[15]Yang C J,Yi H X.Uniqueness theory of meromorphic function[M].New York:Kluwer Academic Publishers,2003.
[2]Hayman W K.Meromorphic functions[M].Oxford:Clarendon Press,1964.
[3]Laine I.Neva,linna theory and complex differential equations[M].Berlin:Walter de Gruyter,1993.
[4]仪洪勋,杨重骏.亚纯函数唯一性理论[M].北京:科学出版社,1995.
[5]Ozawa M.On a solution of w"+e~(-z)w'+(az+b)w=0[J].Kodai Math J,1980,3(2):295-309.
[6]Langley J K.On complex oscillation and a problem of Ozawa[J].Kodai Math J,1986,9(3):430-439.
[7]Gundersen G G.On the question of whether f"+e~(-z)f'+B(z)f=0 can admit a solution f((?)0)of finite order[J].Proc Roy Soc Edinburgh Sect,1986,102(2):9-17.
[8]Gundersen G G.Finite order solutions of second order linear differential equations[J].Trans Amer Math Soc,1988,305(1):415-429.
[9]陈宗煊.微分方程f"+e~(-z)f'+Q(z)f=0解的增长性[J].中国科学:A辑,2001,31(9):775-784.
[10]安蕾,肖丽鹏.一类2阶微分方程的解和小函数的关系[J].江西师范大学学报:自然科学版,2013,37(3):233-235.
[11]袁蓉,刘慧芳.一类二阶非齐次线性微分方程解的复振荡[J].高校应用数学学报:自然科学版,2017,32(4):431-436.
[12]Chen Z X,Shon K H.On the growth of solutions of a class of higher order differential equations[J].Acta Math Sci,2004,24(1):52-60.
[13]Cheng T.The growth of a class of linear differential equation[J].Journal of Fudan University,2006,45(10):610-617.
[14]闵小花,张红霞,易才凤.2阶微分方程的解和小函数的关系[J].江西师范大学学报:自然科学版,2014,38(6):551-556.
[15]Yang C J,Yi H X.Uniqueness theory of meromorphic function[M].New York:Kluwer Academic Publishers,2003.