Asymptotic properties of a class of delay differential equations with a sub-linear neutral term
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摘要: 运用广义Riccati变换和中值定理, 讨论了具有阻尼项的次线性中立型时滞微分方程的振动性及渐近性质. 就参数
$\gamma$ 与$\beta$ 的大小关系和条件$\int^\infty_{t_0}(\frac{1}{R(t)})^{\frac{1}{\gamma}}{\rm{d}}t=\infty$ 的交叉结合在方程振动性的作用方面做了分析, 得到了该方程存在振动解的充分条件, 推广和改进了已有结果, 并用实例给出了其应用.Abstract: This paper studies the oscillation and asymptotic properties of delay differential equations with damping and sub-linear neutral terms using the generalized Riccati transformation technique and the mean value theorem. After analyzing the function of the cross-link between the condition$\int^\infty_{t_0}(\frac{1}{R(t)})^{\frac{1}{\gamma}}{\rm{d}}t=\infty$ and the relationship of parameters$\gamma$ and$\beta$ in the differential equations oscillation, the sufficient conditions for the existence of vibration solutions are provided to extend the existing results in the cited literature. Lastly, some applications are given to illustrate the significance of these results.-
Key words:
- damping /
- delay /
- sub-linear neutral terms /
- differential equations /
- oscillation
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