具有控制系数的高阶线性微分方程复振荡的一个结果

An Oscillation Result for Higher Order Linear Differential Equations with One Dominant Coefficient

该文考虑具有控制系数 A0 和系数仅有有限个极点的高阶线性齐次微分方程 ( 1 .1 ) .得到了一个复振荡结果 ,该结果是 J.K.L angley[11]

The following theorem is known result, if the coefficients are entire (e.g. Bank and Laine for \$k=2,ρ(A\-0)<12\$; Rossi for \$k=2,ρ(A\-0)=12\$; Langley and Hellerstein and coworkers for \$k≥2,ρ(A\-0)≤12).\$In this paper the author will use some new method to prove.Theorem\ Suppose that \$A\-j(j=1,2,\:,k-2)\$ are meromorphic functions with finite poles. If the order \$ρ(A\-0)\$ of \$A\-0\$ is not greater than 12, and \$ρ(A\-j)<ρ(A\-0)\$ for \$j=1,2,\:,k-2\$, then Eq.(1.1) with \$k≥2\$ cannot have two linearly independent solutions each with zero sequence having finite exponent of convergence.