摘要
研究了一类具有有限谱的带有谱参数边界条件的四阶微分方程边值问题及其矩阵表示,证明了对任意正整数m,所考虑的问题至多有2m+6个特征值,进一步给出这类带有谱参数边条件的四阶边值问题与一类矩阵特征值问题之间在具有相同特征值的意义下是等价的.
The matrix representations of a class of fourth order boundary value prob- lems with eigenparameter-dependent boundary conditions which have a finite spectrum are investigated. We first prove that for any positive integer m, the considered problem has at most 2m ＋ 6 eigenvalues. Next, we show that this fourth order boundary value problem with eigenparameter-dependent boundary condition is equivalent to a class of matrix eigenvalue problem in the sense that they have exactly the same eigenvalues.
出处
《数学学报（中文版）》
CSCD
北大核心
2017年第3期427-438,共12页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(11301259
11661059)
内蒙古自然科学基金资助项目(2013MS0105)
关键词
四阶边值问题
矩阵特征值问题
谱参数边条件
有限谱
fourth order boundary value problems
matrix eigenvalue problems
eigenparameter-dependent boundary conditions
finite spectrum
