时标上带有谱参数边界条件的Sturm-Liouville问题的矩阵表示
Matrix Representations of Sturm-Liouville Problems with Eigenparameter-Dependent Boundary Conditions on Time Scales
DOI: 10.12677/AAM.2018.72021, PDF,    国家自然科学基金支持
作者: 刘娜娜, 敖继军, 王 娟：内蒙古工业大学理学院，内蒙古 呼和浩特
关键词: Sturm-Liouville问题；时标；谱参数边界条件；矩阵表示；Sturm-Liouville Problems； Time Scales； Eigenparameter-Dependent Boundary Conditions； Matrix Representations
摘要: 本文讨论了时标上带有谱参数边界条件的Sturm-Liouville问题的矩阵表示。通过分割时标T，使得在对应时标上Sturm-Liouville问题的系数满足特定的条件，得出了所研究的Sturm-Liouville问题与一类矩阵特征值问题之间的等价关系。
Abstract: The matrix representations of Sturm-Liouville problems with eigenparameter-dependent boundary conditions on time scales are investigated. By partitioning the time scales such that the coefficients of Sturm-Liouville equation satisfy some certain conditions on corresponding time scales, the equivalences between Sturm-Liouville problems and a certain kind of matrix eigenvalue problems are obtained.
文章引用：刘娜娜, 敖继军, 王娟. 时标上带有谱参数边界条件的Sturm-Liouville问题的矩阵表示[J]. 应用数学进展, 2018, 7(2): 169-178. https://doi.org/10.12677/AAM.2018.72021

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