| 带谱参数边界条件的四阶边值问题的矩阵表示 |
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| 引用本文： | 敖继军,薄芳珍. 带谱参数边界条件的四阶边值问题的矩阵表示[J]. 数学学报, 2017, 60(3): 427-438 |
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| 作者姓名： | 敖继军 薄芳珍 |
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| 作者单位： | 1. 内蒙古工业大学理学院 呼和浩特 010051;2. 呼和浩特职业学院师范学院 呼和浩特 010051 |
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| 基金项目： | 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） |
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| 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.
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| 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 |
Matrix Representations of Fourth Order Boundary Value Problems with Eigenparameter-Dependent Boundary Conditions |
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| Ji Jun AO,Fang Zhen BO. Matrix Representations of Fourth Order Boundary Value Problems with Eigenparameter-Dependent Boundary Conditions[J]. Acta Mathematica Sinica, 2017, 60(3): 427-438 |
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| Authors: | Ji Jun AO Fang Zhen BO |
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| Affiliation: | 1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, P. R. China;2. Normal College, Hohhot Vocational College, Hohhot 010051, P. R. China |
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| Abstract: | The matrix representations of a class of fourth order boundary value problems 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. |
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| Keywords: | fourth order boundary value problems matrix eigenvalue problems eigenparameter-dependent boundary conditions finite spectrum |
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