关于单位圆内二阶微分方程解的增长性与不动点

Growth and fixed point of solutions for second-order differential-equations in unit-disc

研究了一类单位圆内解析函数系数的二阶线性微分方程解的性质,减弱了系数特征函数的条件,得到了解的超级范围的相同估计;在此基础上,改进了系数条件,得到了解的超级的精确值;并进一步给出了一个常数控制的系数特征函数的新条件类型,得到了解的超级精确值的估计;在上述条件下,还得到了解及其一阶、二阶导数的不动点的精确估计.以上结果改进了曹廷彬和仪洪勋、Benharrat Belaidi的结果.

Second-order linear-differential-equation solutions for one type of analytic-function coefficients in unit-disc are investigated.Conditions of coefficient characteristic functions are extended,same estimates of solution hyper-order range are obtained.The coefficients are improved,hyper-order precise values of solution are obtained.Further,new condition types of one-constant-controlled coefficient characteristic functions are given,hyper-order precise-value estimates of solution are obtained.Under the above conditions,both the solutions,and precise-estimated fixed-points of their 1st and 2nd derivatives are obtained.Our results are a significant improvement over those by Cao Tingbin,Yi Hongxun and Benharrat Belaidi.