时标上具有分布势函数的Sturm-Liouville问题的矩阵表示

Matrix Representations of Sturm-Liouville Problems with Distribution Potentials on Time Scales

本文讨论时标上具有分布势函数的二阶Sturm-Liouville问题的矩阵表示.通过分析得出所研究的具有分布势函数的Sturm-Liouville问题与一类矩阵特征值问题之间的等价关系.文章针对分离型和实耦合型自共轭边界条件分别进行了讨论.

The matrix representations of second order Sturm-Liouville problems with distribution potentials on bounded time scales are investigated. The corresponding equivalences between Sturm- Liouville problems with distribution potentials on time scales and a certain kind of matrix eigenvalue problems are obtained. Both of the separated and coupled self-adjoint boundary conditions are considered to obtain the main results.