洛阳师范学院学报
洛暘師範學院學報
락양사범학원학보
Journal of Luoyang Teachers College
2015年
2期
36~40
,共null页
微分系统 广义特征值 瑞利商 上界 估计
微分繫統 廣義特徵值 瑞利商 上界 估計
미분계통 엄의특정치 서리상 상계 고계
differential system; generalized eigenvalue; Rayleigh quotient; upper bound; estimation
考虑四阶微分系统广义第二特征值的含权上界估计,利用算子的特征值及特征函数空间的定性理论、矩阵运算、分部积分、Schwartz和Young不等式等方法,获得了用第一特征值来估计第二特征值上界的显式不等式,其上界仅与系统的系数有关,而与区间的度量及位置无关,其结果是参考文献结论的进一步拓展.
攷慮四階微分繫統廣義第二特徵值的含權上界估計,利用算子的特徵值及特徵函數空間的定性理論、矩陣運算、分部積分、Schwartz和Young不等式等方法,穫得瞭用第一特徵值來估計第二特徵值上界的顯式不等式,其上界僅與繫統的繫數有關,而與區間的度量及位置無關,其結果是參攷文獻結論的進一步拓展.
고필사계미분계통엄의제이특정치적함권상계고계,이용산자적특정치급특정함수공간적정성이론、구진운산、분부적분、Schwartz화Young불등식등방법,획득료용제일특정치래고계제이특정치상계적현식불등식,기상계부여계통적계수유관,이여구간적도량급위치무관,기결과시삼고문헌결론적진일보탁전.
In consideration of weighted estimate of generalized second eigenvalue＇s upper bound for differential system with fourth-order,the explicit inequality of the upper bound of generalized second eigenvalue is estimated from the first eigenvalue by using qualitative theory of eigenfunction space,matrix operation,integral,Schwartz and Young inequality. This upper bound is dependent only on the coefficients of the system,instead of the measure or location of the interval. The results in the bibliography are improved and extended in this paper.
