Matrix representations of fourth order boundary value problems with finite spectrum

DOI10.1016/j.laa.2011.10.001zbMath1244.34019OpenAlexW2065625832MaRDI QIDQ2427923

Ji-jun Ao, Anton Zettl, Jiong Sun

Publication date: 19 April 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.10.001

zbMATH Keywords

eigenvaluesboundary value problemsmatrix representations

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Eigenvalues, singular values, and eigenvectors (15A18) Weyl theory and its generalizations for ordinary differential equations (34B20) Linear symmetric and selfadjoint operators (unbounded) (47B25) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (12)

Finite Spectrum of 2nth Order Boundary Value Problems with Transmission Conditions ⋮ Matrix representations of Sturm-Liouville problems with coupled eigenparameter-dependent boundary conditions ⋮ The finite spectrum of Sturm-Liouville problems with \(n\) transmission conditions and quadratic eigenparameter-dependent boundary conditions ⋮ Matrix representations of fourth order boundary value problems with periodic boundary conditions ⋮ Equivalence of fourth order boundary value problems and matrix eigenvalue problems ⋮ The finite spectrum of fourth-order boundary value problems with transmission conditions ⋮ Survey article: Self-adjoint ordinary differential operators and their spectrum ⋮ Matrix representations of fourth-order boundary value problems with transmission conditions ⋮ Matrix representations of fourth-order boundary value problems with coupled or mixed boundary conditions ⋮ Eigenvalues of a class of fourth-order boundary value problems with transmission conditions using matrix theory ⋮ Unnamed Item ⋮ Finite spectrum of \(2 n\)th order boundary value problems

Cites Work

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• Fourth order canonical forms of singular self-adjoint boundary conditions
• The study of Jacobi and cyclic Jacobi matrix eigenvalue problems using Sturm-Liouville theory
• Matrix representations of Sturm-Liouville problems with finite spectrum
• The classification of self-adjoint boundary conditions: separated, coupled, and mixed
• Characterization of domains of self-adjoint ordinary differential operators
• Spectral theory of ordinary differential operators
• Dependence of the \(n\)th Sturm-Liouville eigenvalue on the problem
• Floquet theory for left-definite Sturm-Liouville problems
• Numerical methods for higher order Sturm-Liouville problems
• Characterization of domains of self-adjoint ordinary differential operators. II
• Discrete and continuous boundary problems
• Sturm-Liouville problems with finite spectrum

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