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Zheng, Zhaowen; Cai, Jinming; Li, Kun; Zhang, Maozhu

A discontinuous Sturm-Liouville problem with boundary conditions rationally dependent on the eigenparameter. (English) Zbl 1499.34206

Bound. Value Probl. 2018, Paper No. 103, 15 p. (2018).
Summary: 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.

Cited in 12 Documents

MSC:

34B24 Sturm-Liouville theory
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
47E05 General theory of ordinary differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators

Keywords:

Sturm-Liouville problem; eigenparameter dependent boundary condition; transmission condition; asymptotic formulae of eigenvalue and eigenfunction; completeness
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References:

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