一类正则Sturm-Liouville问题特征值精细的渐近估计

Asymptotic Behavior of Eigenvalues of A Sturm-Liouville Problem with Regular Boundary

考虑[0,π]上一类带一般分离型边界条件的正则Sturm-Liouville问题特征的渐近表示.利用Frechet导数,对该问题的特征值和特征函数进行了更为精细的分析,讨论了实值函数q(x)∈L2[0,π]及边界条件中常数cotα和cotβ对特征值、特征函数的影响.

We consider the asymptotic expansion of eigenvalues for a regular Sturm-Liouville Problem on [0,π].By combining Frechet derivative,we give a sophisticated analysis for the eigenvalues,which reveals the explicit effects of boundary independence and equation coefficient.