一类带分布时滞的非线性中立型广义弹性杆方程的振动分析

Oscillatory Analysis for a Class of Nonlinear Neutral Generalized Elastic-Rod Equations with Distributed Delay

基于力学上非线性弹性杆(组)结构的振动问题与数学上偏微分方程(组)振动理论之间的密切联系,研究了一类带分布时滞的偶数阶非线性中立型广义弹性杆方程的振动性问题,建立了该类弹性杆方程在Dirichlet边值条件下所有解振动的新的充分性判据,并给出一个实例阐述结果的有效性.所得结果反映出该类弹性杆结构在这种情况下的振动状态——它始终发生振动.

Based on the close relationship between the vibration problems of nonlinear elastic rod(systems)structure in mechanics and the oscillation theory of partial differential equation(systems)in mathematics,the oscillation problems for a class of even order nonlinear neutral generalized elastic-rod equations with distributed delays are investigated,and some new sufficient criteria for oscillation of all solutions of such elastic-rod equations are establish under Dirichlet’s boundary value condition,which the effectiveness of the results is illustrated by an example.The obtained results reflect the oscillation state of such elastic-rod structure in the case that the oscillation kept happening.