A discontinuous Sturm-Liouville problem with boundary conditions rationally dependent on the eigenparameter

DOI10.1186/s13661-018-1023-xzbMath1499.34206OpenAlexW2810310033MaRDI QIDQ2126413

Kun Li, Jinming Cai, Zhaowen Zheng, Mao-Zhu Zhang

Publication date: 19 April 2022

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-018-1023-x

zbMATH Keywords

completenessSturm-Liouville problemeigenparameter dependent boundary conditiontransmission conditionasymptotic formulae of eigenvalue and eigenfunction

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) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items

Regular approximation of singular Sturm-Liouville problems with eigenparameter dependent boundary conditions ⋮ Computation of eigenvalues and eigenfunctions of a non-local boundary value problem with retarded argument ⋮ The inverse problem for the heat equation with reflection of the argument and with a complex coefficient ⋮ A generalized discontinuous Sturm-Liouville problem with boundary conditions rationally dependent on the eigenparameter ⋮ Asymptotic analysis of Sturm-Liouville problem with Neumann and nonlocal two-point boundary conditions ⋮ ON THE EIGENVALUES AND THE NODAL POINTS OF THE EIGENFUNCTIONS OF SOME EIGENVALUE PROBLEMS WITH EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS ⋮ Completeness theorem for eigenparameter dependent dissipative Dirac operator with general transfer conditions ⋮ Inverse spectral problem for Sturm-Liouville operator with coupled eigenparameter-dependent boundary conditions of Atkinson type ⋮ ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND EIGENFUNCTIONS OF A NONLOCAL BOUNDARY VALUE PROBLEM ⋮ Solvability and coerciveness of multi-point Sturm-Liouville problems with abstract linear functionals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sturm-Liouville problems with eigendependent boundary and transmissions conditions
• Oscillation criteria for forced second order differential equations with mixed nonlinearities
• Dependence of eigenvalues of Sturm- Liouville problems with interface conditions
• The basis property of the system of weak eigenfunctions of a discontinuous Sturm-Liouville problem
• Variational principles for spectral analysis of one Sturm-Liouville problem with transmission conditions
• Nonselfadjoint spectral problems for linear pencils \(N- \lambda P\) of ordinary differential operators with \(\lambda\)-linear boundary conditions: Completeness results
• Sturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter. II
• Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions
• Spectral analysis for discontinuous non-self-adjoint singular Dirac operators with eigenparameter dependent boundary condition
• A singular Sturm-Liouville problem with limit circle endpoints and eigenparameter dependent boundary conditions
• Dependence of eigenvalues of \(2m\)th-order spectral problems
• Sturm-Liouville problems with discontinuities at two points
• Regular eigenvalue problems with eigenvalue parameter in the boundary condition
• Asymptotic behavior of a differential operator with discontinuities at two points
• Classification of Sturm–Liouville differential equations with complex coefficients and operator realizations
• Inverse problems for Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter
• Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
• STURM–LIOUVILLE PROBLEMS WITH BOUNDARY CONDITIONS RATIONALLY DEPENDENT ON THE EIGENPARAMETER. I
• Problems for Ordinary Differential Equations with Transmission Conditions
• Eigenvalues of regular fourth‐order Sturm–Liouville problems with transmission conditions
• The eigenvalue problem with interaction conditions at one interior singular point
• Resolvent operator and spectrum of new type boundary value problems

This page was built for publication: A discontinuous Sturm-Liouville problem with boundary conditions rationally dependent on the eigenparameter