长春大学学报(自然科学版)
長春大學學報(自然科學版)
장춘대학학보(자연과학판)
JOURNAL OF CHANGCHUN UNIVERSITY
2009年
3期
52-54,59
,共4页
六阶微分方程%特征值%特征函数%上界%估计
六階微分方程%特徵值%特徵函數%上界%估計
륙계미분방정%특정치%특정함수%상계%고계
differential equation with six orders%eigenvalue%eigenfunction%upper bound%estimation
考虑六阶常微分方程广义第二特征值的上界估计.利用试验函数,Rayleigh定理,分部积分和Schwartz不等式等估计方法与技巧,获得了用第一特征值来估计第二特征值的上界的不等式,其估计系数与区间的度量无关.其结果在物理学和力学中有着广泛的应用,在常微分方程的研究中起着重要的作用.
攷慮六階常微分方程廣義第二特徵值的上界估計.利用試驗函數,Rayleigh定理,分部積分和Schwartz不等式等估計方法與技巧,穫得瞭用第一特徵值來估計第二特徵值的上界的不等式,其估計繫數與區間的度量無關.其結果在物理學和力學中有著廣汎的應用,在常微分方程的研究中起著重要的作用.
고필륙계상미분방정엄의제이특정치적상계고계.이용시험함수,Rayleigh정리,분부적분화Schwartz불등식등고계방법여기교,획득료용제일특정치래고계제이특정치적상계적불등식,기고계계수여구간적도량무관.기결과재물이학화역학중유착엄범적응용,재상미분방정적연구중기착중요적작용.
The paper presents the estimation of the upper bound of generalized second eigenvalue for the differential equation with six orders. The upper of second eigenvalue is dependent on the first eigenvalue based on integral, Rayleigh theorem and inequality estima-tion. The estimation coefficients do not depend on the measure of the domain in which the problem is concerned. This kind of problem is significant both in theory of differential equations and in application to mechanics and physics, which plays an important role in the research of ordinary differential equation.
