正則高階微分系統(tǒng)帶權(quán)第二特征值的上界

朱敏峰，錢椿林

(蘇州市職業(yè)大學(xué) 基礎(chǔ)部，江蘇 蘇州 215104)

正則高階微分系統(tǒng)帶權(quán)第二特征值的上界

朱敏峰，錢椿林

(蘇州市職業(yè)大學(xué) 基礎(chǔ)部，江蘇 蘇州 215104)

考慮正則高階微分系統(tǒng)帶權(quán)第二特征值的上界估計(jì).利用試驗(yàn)函數(shù)、Rayleigh定理、分部積分和Schwarz 不等式等估計(jì)方法與技巧，獲得了用第一特征值來估計(jì)第二特征值的上界的不等式，其估計(jì)系數(shù)與區(qū)間的度量無關(guān).其結(jié)果在物理學(xué)和力學(xué)中有著廣泛的應(yīng)用，在常微分方程的研究中起著重要的作用.

正則高階微分系統(tǒng)；特征值；特征向量；上界

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[2]HILE G N，YEN R Z. Inequalities for eigenvalue of the Biharmonic operator[J]. Pacific J.Math，1984 (1)：115-133.

[3]PROTTER M H. Can one hear the shape of a drum? [J]. SIAM Rev，1987 (2)：185-197.

Upper Bound of Second Eigenvalue with Weight for the Canonical Differential System with High Orders

ZHU Min-feng，QIAN Chun-lin

(Department of Basic Education，Suzhou Vocational University，Suzhou 215104，China)

This paper considers the estimation of the upper bound of second eigenvalue for the canonical differential system with high orders.The upper of second eigenvalue is dependent on the first eigenvalue by using integral，rayleigh theorem and inequality estimation.The estimation coefficients do not depend on the measure of the domain its which the problem is concerned.This kind of problem is significant both in theory of differential equations and in application to mechanics and physics.

canonical differential system with high orders；eigenvalue；eigenvector；the upper bound

O175.1

A

1008-5475(2012)04-0030-07

2012-08-06；

2012-09-05

蘇州市職業(yè)大學(xué)青年基金資助項(xiàng)目(2010SZDQ12)

朱敏峰(1981-)，男，江蘇蘇州人，講師,碩士研究生,主要從事算子特征值估計(jì)研究.

(責(zé)任編輯：沈鳳英)