高阶具非线性中立项不稳定型时滞微分方程的振动性和非振动性

Oscillatory and Nonoscillatory of High-order Unstable Delay Differential Qquations with Nonlinear Neutral Term

在α>1,且0<β<α情性下研究了高阶具非线性中立项不稳定型时滞微分方程[x(t)-pxα(t-τ)](n)=q(t)xβ(t-σ),(t≥t0)的振动和非振动性.利用一些新的技巧,获得了上述方程有界解振动的振动准则和至少存在一个非振动解的非振动准则,所得结果补充和推广了已有文献部分结果.

The oscillatory and non-oscillatory criteria of high-order unstable Delay Differential equations with nonlinear neutral term[r（f）-px^α（t-r）]^（m）=q（t）x^β（t-σ）.（t≥t0） to is studied in the csse when a 〉 I and 0 〈 β 〈 a. By suing some new technique, some oscillatory criteria are obtaind and a non-oscillatory criteria that there exists at least a non-oscillatory solution is obtaind. These results fill a gap in the literature.