具变系数的二阶中立型微分方程解的振动性

OSCILLATIONS OF SOLUTIONS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

本文研究具有变系数的二阶非线性中立型方程和线性中立型方程建立了方程(1)和(16)的所有有界解振动的充分条件,其条件是“sharp"的,也给出了方程(1)的线性化极限振动准则。所得结果推广了文《二阶非线性中立型微分方程解的振动准则》(钱祥征等,湖南教学年刊Vol.10No.1—2,(1990),101—108)中的结论。

In this paper, we consider the second order nonlinear neutral equation. (1) and linear neutral equation (16) We establish some safficient conditions for all bonnded solutions of Eq. (1)and (16) to oscillate and the conditions are 'sharp'. We also give linearized oscillation criteria of Eq. (1). We generalize the results in [1].