【摘要】 利用试验函数、分部积分、Rayleigh定理和不等式估计等方法与技巧,获得了用第一个特征值来估计第二个特征值的上界的结果,其估计系数与区域的几何度量无关,其结果在物理学和力学等领域中应用广泛,G.H.Hile和R.Z.Yeh所得的结果是本文的特例。更多还原

【Abstract】 This paper considers the estimate for the upper bound of second eigenvalue of a certain differential systems. The inequality of the upper bound of second eigenvalue is estimated from first eigenvalue 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. This kind of problem is significant in the potential application to mechanics and physics. The results obtained by G. H. Hile and R. Z. Yehare only a special case of ours.更多还原