单位圆内非齐次线性微分方程的振荡解

Oscillatory Solutions of Nonhomogeneous Linear Differential Equation in the Unit Disc

研究了单位圆内高阶非齐次线性微分方程的振荡解,得到了方程f(k)+ak-1f(k-1)+…+a0f=F(a0,a1,…,ak-1和F是单位圆内的亚纯函数)具有1个振荡解空间,其空间中所有解的零点收敛指数为∞,至多除去1个例外值.

The oscillatory solutions of higher-order nonhomogeneous linear differential equation in the unit disc arediscussed. Results concerning the equation f（k）＋ak-1f（k-1）＋…＋a0f=F（a0,a1,…,ak-1 and Fare meromorphic functions in the unit disc）, and possessing an oscillatory solution subspace in which all solutions （which at most one exception） have infinite exponent of convergence of zeros are obtained.