摘要
运用施图姆-刘维尔谱理论,对偶阶含权微分系统的低阶离散谱进行定量估计,首先,利用瑞利商原理得到一基本不等式,其次估计了若干积分式的上界或下界,为提高估计的精度,引入了一正参数δ,最后获得了用主谱的二次多项式来估计次谱的上界不等式,其结果是相关文献结论的进一步拓展。
With the help of Sturm-Liouville’s spectrum theory,the quantitative estimate of the lower order spectra for even-order weighted differential system was considered.We first gained a basic inequality according to the Rayleigh quotient theorem.Secondly,the upper or lower bounds of several integrals were estimated.For the more precision,we introduced a positive parameterδ.At last,the inequality of the explicit upper bound of the secondary spectrum estimated from the quadratic polynomial of principal spectrum was obtained.The results in the bibliography are improved and extended in this paper.
作者
黄振明
HUANG Zhengming(Department of Mathematics and Physics,Suzhou Vocational University,Suzhou 215104,China)
出处
《东莞理工学院学报》
2018年第1期8-13,共6页
Journal of Dongguan University of Technology
关键词
偶阶微分系统
次谱
瑞利商原理
定量估计
上界不等式
even-order differential system
secondary spectrum
Rayleigh quotient theorem
quantitative estimate
upper bound inequality
