Variational principles for spectral analysis of one Sturm-Liouville problem with transmission conditions

DOI10.1186/s13662-016-0800-zzbMath1419.34105OpenAlexW2300595940WikidataQ59438104 ScholiaQ59438104MaRDI QIDQ1796773

Kadriye Aydemir, Oktay Sh. Mukhtarov

Publication date: 17 October 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-016-0800-z

zbMATH Keywords

Sturm-Liouville problemstransmission conditionsboundary-transmission conditionsParseval equalityCarleman equationexpansions theoremRayleigh-Ritz formula

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General theory of ordinary differential operators (47E05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Green's functions for ordinary differential equations (34B27) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (11)

A discontinuous Sturm-Liouville problem with boundary conditions rationally dependent on the eigenparameter ⋮ Basicity properties of eigenfunctions of the periodic problem for differential operator Lu = −u″(−x) + q(x)u(x) ⋮ A singular Sturm-Liouville problem with limit circle endpoint and boundary conditions rationally dependent on the eigenparameter ⋮ Dependence of eigenvalues of 2\(n\)th order boundary value transmission problems ⋮ Asymptotic behavior for eigenvalues of the singular Sturm-Liouville problem with transmission conditions ⋮ Direct approach for the characteristic function of a dissipative operator with distributional potentials ⋮ Weak eigenfunctions of two-interval Sturm-Liouville problems together with interaction conditions ⋮ ON THE EIGENVALUES AND THE NODAL POINTS OF THE EIGENFUNCTIONS OF SOME EIGENVALUE PROBLEMS WITH EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS ⋮ Computing high-index eigenvalues of singular Sturm-Liouville problems ⋮ Completeness theorem for eigenparameter dependent dissipative Dirac operator with general transfer conditions ⋮ Eigenvalues of regular fourth‐order Sturm–Liouville problems with transmission conditions

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