Publication: Spectral Properties of Discontinuous Sturm–Liouville Problems with a Finite Number of Transmission Conditions
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Springer Science and Business Media LLC
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The authors investigate the eigenvalues and eigenfunctions of a discontinuous eigenvalue problem consisting of a Sturm-Liouville problem with eigenparameter-dependent boundary conditions and transmission conditions at points of discontinuity. The self-adjoint linear operator is defined in a suitable Hilbert space and asymptotic formulas for eigenvalues and eigenfunctions are derived. The completeness of the eigenfunctions are also analyzed.
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transmission conditions, General theory of ordinary differential operators, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators, spectrum, Sturm-Liouville theory, asymptotics of eigenvalues and eigenfunctions, completeness, Green's functions for ordinary differential equations, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, eigenparameter-dependent boundary conditions, Sturm-Liouville problems