Error estimate of eigenvalues of perturbed second-order discrete Sturm–Liouville problems |
| |
Authors: | Haiyan Lv Yuming Shi |
| |
Affiliation: | School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China |
| |
Abstract: | This paper is concerned with eigenvalues of perturbed second-order vector discrete Sturm–Liouville problems. By some variational properties of eigenvalues of discrete Sturm–Liouville problems, error estimates of eigenvalues of perturbed problems, sufficiently close to a given Sturm–Liouville problem, are given under a certain non-singularity condition. Perturbations of the coefficient functions of the difference equation, the weight function, and the coefficients of the boundary condition are all considered. This, together with higher-dimension involved, results in a certain complexity of the problem and difficulty of study. As a direct consequence, continuous dependence of eigenvalues on problems is obtained under the non-singularity condition. In addition, an example is presented to illustrate the necessity of the non-singularity condition. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|