高阶微分方程第二特征值的上界  

Upper Bound of the Second Characteristic Value of Higher Differential Equation

作　　者：俞金元[1] 

机构地区：[1]江苏广播电视大学基础部

出　　处：《南京航空航天大学学报》1998年第5期507-514,共8页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：设（ａ，ｂ）Ｒ是一个有界开区间，考虑如下的特征值问题∑ｔｋ＝ｒ＋１（－１）ｋＤｋ（Ｐｋ（ｘ）Ｄｋｙ）＝λ（－１）ｒＤ２ｒｙ，ｘ∈（ａ，ｂ）Ｄｋｙ（ａ）＝Ｄｋｙ（ｂ）＝０，ｋ＝０，１，…，ｔ－１其中ｔ，ｒ均为正整数，且ｔ＞ｒ≥１，Ｐｋ（ｘ）满足某些条件（ｋ＝ｒ＋１，ｒ＋２，…，ｔ）。利用这些条件，运用某些著名不等式和分析技巧，对本文中的变系数微分方程的特征值估计问题，建立了用第一特征值λ１来估计第二特征值λ２（λ１≤λ２）的不等式，其估计系数与区间度量无关，其结果在物理和力学领域中有着广泛的用途。?a,b)R is assumed to be one bounded open interval,the following problem about characteristic values is considered[FC({〗∑tk=r+1(-1) kD k(P k(x)D ky)=λ(-1) rD 2r y x∈(a,b) D ky(a)=D ky(b)=0 k=0,1,…,t-1in which both t and r are positive integers,and t>r≥1.P k(x) satisties some conditions (k=r+1,r+2,…,t).With the help of some famous inequalities and analysis techniques, one inequality is established about the characteristic value estimation for the differential equations with variable coefficients presented in this paper based on these conditions.The inequality is used to estimate the second characteristic value λ 2(λ 1≤λ 2) from the first characteristic value λ 1.Its coefficient of estimation has nothing to do with the measure of interval. The result has wide application in physics and mechanics.

关 键 词：特征值 高阶微分方程 特征函数 上界 

分 类 号：O175.9[理学—数学] O175.1[理学—基础数学]