边界条件含特征参数的奇异不连续Sturm-Liouville算子的渐近特征

Asymptotic Behaviors of a Second Order Singular Discontinuous Differential Operator with Eigenparameter Dependent Boundary Conditions

研究有限区间内一类边界条件含特征参数的不连续奇异Sturm-Liouville问题.利用函数论和算子理论的方法,证明该问题的自伴性,得到其特征值的相关性质,基本解及其特征值的渐近公式.

In this paper Strum-Liouville problem with eigenparameter dependent boundary conditions and with transmission conditions at finite points of considered finite interval is obtained. We prove that it＇s self-adjoint in a adequate Hilbert Space differential operator generated by this Singular Sturm-Liouville problem. Then some properties of the eigenvalues and asymptotic formulas for fundamental solutions and eigenvalues of the considered problem be investigated with function theory and operator method.