一类二阶非齐次线性微分方程解的复振荡

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.

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

In this paper, the growth and the distribution of zeros of solutions to some second order non-homogeneous differential equations f″+Aeaznf′+(B1ebzn +B0edzn)f =F(z) are investigated, where F is a nonzero entire function with order less than n, A, B1, B0 are 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.