The spectrum of singular Sturm-Liouville problems with eigenparameter dependent boundary conditions and its approximation

DOI10.1007/s00025-012-0270-xzbMath1273.34034OpenAlexW2089586406MaRDI QIDQ351138

Zhang Maozhu, Jiong Sun, Anton Zettl

Publication date: 11 July 2013

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-012-0270-x

zbMATH Keywords

essential spectrumeigendependent boundary conditionsnorm resolvent convergenceregular approximationssingular Sturm-Liouville problemstrong resolvent convergence

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16)

Related Items (13)

New convergence mode for the generalized spectrum approximation ⋮ Regular approximation of singular Sturm-Liouville problems with eigenparameter dependent boundary conditions ⋮ Regular approximation of singular Sturm-Liouville problems with transmission conditions ⋮ Completeness of eigenfunctions of discontinuous Sturm-Liouville problems ⋮ The basis property of the system of weak eigenfunctions of a discontinuous Sturm-Liouville problem ⋮ Dependence of eigenvalues of Sturm-Liouville problems with eigenparameter dependent boundary conditions ⋮ Regular approximation of singular third-order differential operators ⋮ A generalized discontinuous Sturm-Liouville problem with boundary conditions rationally dependent on the eigenparameter ⋮ Dissipative operator and its Cayley transform ⋮ On the numerical treatment of the eigenparameter dependent boundary conditions ⋮ SELF-ADJOINT REALIZATION OF A CLASS OF THIRD-ORDER DIFFERENTIAL OPERATORS WITH AN EIGENPARAMETER CONTAINED IN THE BOUNDARY CONDITIONS ⋮ Regular approximation of linear Hamiltonian operators with two singular endpoints ⋮ Fourth order differential operators with distributional potentials

Cites Work

• Characterization of domains of self-adjoint ordinary differential operators
• Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions
• Equivalence of inverse Sturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter.
• Sturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter. II
• Regular approximations of singular Sturm-Liouville problems
• Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions
• Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
• Sturm–Liouville problems with eigenparameter dependent boundary conditions
• Asymptotics of the m -Coefficient for Eigenvalue Problems with Eigenparameter in the Boundary Conditions
• Algorithm 810: The SLEIGN2 Sturm-Liouville Code
• Inequalities and eigenvalues of Sturm-Liouville problems near a singular boundary
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