关于方程f″+P(z)f′+Q(z)f=0的解的复振荡性质

On Complex Oscillation Properties ofSolutions of f″+P (z) f′+ Q (z) f=0

本文着重研究了二阶线性微分方程 f″+P(z)f′+Q(z)f=0(其中P(z)、Q(z)为多项式)的解的复振荡性质,即其解的零点收敛指数与增长级的比较,得到了一些结果。同时,本文还研究了方程f″+P(z)f=0(其中P(z)为多项式,且degP=p>0)具有一非平凡解f_0使得λ(f_0)<p+2/2时的特性。(其中λ(f_0)表示f_0的零点收敛指数)。

The second-order linear differential equation f″+ P (z)f′+ Q (z)f=0 is studiedwhere P(z) and Q(z) are polynomials. The complex oscillation properties of itssolutions, i. e. the comparison of the convergence-exponent of zeros to its order ofgrowth are obtained. The characteristics of the equation f″+P(z)f=0 possessingone non-trivial solution f_0 with λ(f_0)<(p+2)/2 are also considered, where P(z)is a polynomial with degree p>0 and λ(f_0) denotes the convergence-expon()nt ofzeros of f_0.