No abstract

The present paper deals with a class of discontinuous Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter. Operator formulation is built and asymptotic formulas for eigenvalues and eigenfunctions are given. Moreover, the completeness of its eigenfunctions is also discussed.

This note presents exact frequency equations of two independent classes of vibrations of a spherically isotropic solid sphere with fixed boundary conditions. Numerical calculations are performed and comparison between two different materials is made. Some useful observations are obtained. [S0021-8936(00)00102-1]

We study matrix representations of Sturm-Liouville problems with coupled eigenparameter-dependent boundary conditions and transmission conditions. Meanwhile, given any matrix eigenvalue problem with coupled eigenparameter-dependent boundary conditions and transmission conditions, we construct a class of Sturm-Liouville problems with given boundary conditions and transmission conditions such that they have the same eigenvalues.

In this paper, we investigate a class of discontinuous singular Sturm-Liouville problems with limit circle endpoints and eigenparameter dependent boundary conditions. Operator formulation is constructed and asymptotic formulas for eigenvalues and fundamental solutions are given. Moreover, the completeness of eigenfunctions is discussed.