通化师范学院学报
通化師範學院學報
통화사범학원학보
JOURNAL OF TONGHUA TEACHERS COLLEGE
2014年
6期
24-27
,共4页
微分方程%主%次特征值%下界%估计
微分方程%主%次特徵值%下界%估計
미분방정%주%차특정치%하계%고계
differential equation%principal and secondary eigenvalue%lower bound%estimate
考虑偶数阶微分方程在 Dirichlet 和 Neumann 边界条件下广义特征值的估计，利用方程特征值理论、分部积分、测试函数、广义 Rayleigh 定理和不等式估计等方法，获得了主次特征值之比的下界估计不等式，且估计值与区间的几何量无关。
攷慮偶數階微分方程在 Dirichlet 和 Neumann 邊界條件下廣義特徵值的估計，利用方程特徵值理論、分部積分、測試函數、廣義 Rayleigh 定理和不等式估計等方法，穫得瞭主次特徵值之比的下界估計不等式，且估計值與區間的幾何量無關。
고필우수계미분방정재 Dirichlet 화 Neumann 변계조건하엄의특정치적고계，이용방정특정치이론、분부적분、측시함수、엄의 Rayleigh 정리화불등식고계등방법，획득료주차특정치지비적하계고계불등식，차고계치여구간적궤하량무관。
This paper presents the generalized eigenvalue estimate for even - order differential equation under the Neumann boundary condition as well as Dirichlet. The inequality of the lower bound of the ratio of princi-pal eigenvalue to secondary eigenvalue is estimated by using eigenvalue theory of equation,integration by parts,trial function,generalized Rayleigh theorem and inequality estimate etc. The estimate is irrelevant to the geometric sense of the domain.
