摘要
运用常微分方程特征值的基本理论,考虑一类高阶方程特征值的上界估计,此类方程包含了常见的梁横向震动方程,有着重要的实际背景,利用分部积分、Rayleigh定理和不等式估计等方法,获得了用前n个特征值来估计第n+1个特征值的上界的不等式,其估计系数与区间的几何度量无关,其结果在物理学和力学等领域中应用广泛。
This paper considers the upper bound of eigenvalues for a class of differential equation with higher orders by using the basic theory concerning the eigenvalues of ordinary differential equation. The equation includes the commonly encountered horizontal vibration equation of beam. It has a very important practical background. The inequality of the upper bound of the （n＋1）th eigenvalue is estimated from the first n eigenvalues by using integral, Rayleigh theorem and inequality estimation. The estimate coefficients do not depend on the measure of the domain in which the problem is concerned. The result has a wide application both in physics and mechanics.
出处
《苏州科技学院学报（自然科学版）》
CAS
2006年第1期30-34,44,共6页
Journal of Suzhou University of Science and Technology （Natural Science Edition）
关键词
高阶常微分方程
特征值
上界
估计
differential equation with higher order
eigenvalue
upper bound
estimates
