时间尺度上具有次线性中立项的三阶Emden-Fowler时滞动力方程的振动性

Oscillation of Third-order Nonlinear Emden-Fowler Delay Dynamic Equation with a Sublinear Neutral Term on Time Scales

判定时间尺度上时滞动力方程的振动性和渐近性在数学物理、自动控制理论及工程、传染病模型分析和桥梁设计等诸多领域具有重要作用。针对时间尺度上具有次线性中立项的三阶Emden-Fowler时滞动力方程的振动性和渐近性开展研究,利用时间尺度上的微积分理论,广义Riccati变换和不等式技巧,获得了该方程两个振动定理,改进和推广了已有文献的相应结果,并给出了两个实例验证了新定理的有效性。

Judging the oscillation and asymptotic behavior of delay dynamic equations on time scale plays an important role in mathematical physics,automatic control theory and engineering,infectious disease model analysis,bridge design and so on.Thus,the oscillation behavior of third-order nonlinear Emden-Fowler type delay dynamic equation with a sublinear neutral term on time scales are investigated.By using the dynamic calculus on time scales,generalized Riccati transformation and inequality technique,two oscillation theorems to ensure that every solution of the equation oscillates or converges to zero are obtained.These results extend and improve the results established in previous literatures.Finally,the effectiveness of the theoretical results obtained here are illustrated with two examples.