一类二阶非齐次线性微分方程解的复振荡  

Complex oscillation of solutions of some second order non-homogeneous linear differential equations

作　　者：袁蓉[1] 刘慧芳[1] YUAN Rong;LIU Hui-fang(College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022,China)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《高校应用数学学报（A辑）》2017年第4期431-436,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11661044)

摘　　要：研究了一类二阶非齐次线性微分方程f″+Ae^(az^n)f′+(B_1e^(bz^n)+B_0e^(dz^n))f=F(z)解的增长性和零点分布,其中F为级小于n的非零整函数,A,B1,B0为非零多项式.在复数a,b,d满足一定条件下,得到该方程的每一个解的超级和二级零点收敛指数的精确估计.In this paper,the growth and the distribution of zeros of solutions to some second order non-homogeneous differential equations f00+Aeaznf0+(B1ebzn+B0edzn)f=F(z)are investigated,where F is a nonzero entire function with order less than n,A;B1;B0are nonzero polynomials.Under an appropriate assumption on complex numbers a;b;d,the precise estimations on the hyper order and the hyper convergence exponent of zeros of solutions of such equation are obtained.

关 键 词：微分方程 整函数 超级 零点 

分 类 号：O175.14[理学—数学]