一类Sturm-Liouville问题的特征值的渐近分析

Asymptotic analysis of the eigenvalue of a class of Sturm-Liouville problem

目的讨论一类有限区间[0,π]上的常型Sturm-Liouville算子特征值的渐近估计。方法本文运用了同阶无穷小的比较法。结果得到了一类有限区间[0,π]上的常型Sturm-Liouville问题比较精细的特征值的渐近估计。结论给出了微分方程系数及边条件对特征值的影响。

Objective-To discuss the asymptotic formulas for the eigenvalues of a class of regular Sturm-Liouville problem defined on [O, π]. Methods-The method of comparison with infinitesimal of the same order is used for the said objective. Results-The asymptotic estimation of the eigenvalues of such kind of Sturm Liouville problems is obtained. Conclusion-It is shown that the eigenvalues de pend not only on the coefficients of differential equation but also on the boundary conditions.