Spectral theory of higher-order discrete vector Sturm-Liouville problems

DOI10.1016/S0024-3795(00)00256-1zbMath0977.39010MaRDI QIDQ5929754

Yuming Shi, Shaozhu Chen

Publication date: 21 January 2002

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

zbMATH Keywords

eigenvaluesboundary value problemspectral theorycomparison theoremsdifference operatorhigher-order vector difference equationsself-adjoint operatorSturm-Liouville problems

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Discrete version of topics in analysis (39A12) Difference operators (39A70) Linear difference operators (47B39)

Related Items (12)

Dependence of eigenvalues of certain closely discrete Sturm-Liouville problems ⋮ Eigenvalue comparisons for second order difference equations with Neumann boundary conditions ⋮ Continuous dependence of the \(n\)-th eigenvalue of self-adjoint discrete Sturm-Liouville problems on the problem ⋮ The Glazman--Krein--Naimark theory for a class of discrete Hamiltonian systems ⋮ Eigenvalue comparisons for a class of boundary value problems of second order difference equations ⋮ Spectral properties of a boundary value problem for the discrete beam equation ⋮ Error estimate of eigenvalues of perturbed higher-order discrete vector boundary value problems ⋮ Eigenvalue comparisons for second order difference equations with periodic and antiperiodic boundary conditions ⋮ Weyl--Titchmarsh theory for a class of discrete linear Hamiltonian systems ⋮ Inequalities among eigenvalues of different self-adjoint discrete Sturm-Liouville problems ⋮ Oscillation of self-adjoint second-order vector difference equations to the parameter ⋮ Existence and uniqueness of positive solitons for a second-order difference equation

Cites Work

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• Sturmian theory for ordinary differential equations
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• Dependence of the \(n\)th Sturm-Liouville eigenvalue on the problem
• Spectral theory of second-order vector difference equations
• Discrete linear Hamiltonian eigenvalue problems
• Discrete and continuous boundary problems
• Boundary Value Problems for annth Order Linear Difference Equation
• A TREATMENT OF STURM-LIOUVILLE EIGENVALUE PROBLEMS VIA PICONE'S IDENTITY
• Difference Equations: Disconjugacy, Principal Solutions, Green's Functions, Complete Monotonicity
• Oscillation and Nonoscillation for Systems of Self-Adjoint Second-Order Difference Equations
• Oscillation criteria for higher order sturm–liouville difference equations^*
• Second-order Sturm-Liouville difference equations and orthogonal polynomials
• On the unboundedness below of the Sturm—Liouville operator
• On an Ordinary Differential Equation Involving a Convex Function

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