一类右定Sturm-Liouville算子特征的渐近分析

Asymptotic Behavior of a Right-definite Sturm-Liouville Problem

考虑[0,π]上一类带一般分离型边界条件的右定S-L问题特征值的渐近表示,利用Green-Liouville变换及Fréchet导数,对特征值进行精细的分析,清楚地给出了方程系数q(x)与权函数w(x)及边界条件中常数cotα,cotβ对特征值的影响,使结论更具一般化.

The asymptotic expansion of eigenvalues for a right-definite Stirm-Liouville problem in [-0, π] is considered. Combined the Green-Liouville transformation and Frechet derivative together,a sophisticated analysis for the eigenvalues is obtained to reveal the explicit effects of the boundary condition ,the weight function and equation coefficient.