Half-range solutions of indefinite Sturm-Liouville problems

DOI10.1016/0022-1236(87)90113-3zbMath0619.35062OpenAlexW2063271575MaRDI QIDQ1089512

Martin Klaus, Cornelis V. M. van der Mee, Vladimir A. Protopopescu

Publication date: 1987

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(87)90113-3

zbMATH Keywords

eigenfunction expansionindefinite weight functionexplicit representationsdiffusion equations of Sturm-Liouville typefinitely many sign changesWiener-Hopf-type integral equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Integral representations of solutions to PDEs (35C15) Solutions to PDEs in closed form (35C05)

Related Items (7)

Transfer functions and operator theory ⋮ Numerical Experiments with the Fokker–Planck Equation in 1D Slab Geometry ⋮ A class of linear kinetic equations in a Krein space setting ⋮ Indefinite elliptic spectral problems ⋮ Abstract Kinetic Equations with Positive Collision Operators ⋮ Full range solution of half space neutron transport problem ⋮ Direct versus iterative methods for forward-backward diffusion equations. Numerical comparisons

Cites Work

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• Generalized kinetic equations
• Half-range completeness for the Fokker-Planck equation. I
• Strong solutions of stationary equations in abstract kinetic theory
• Minimal factorization of matrix and operator functions
• An abstract treatment of some forward-backward problems of transport and scattering
• Spectral analysis of the transport equation. I. Nondegenerate and multigroup case
• On an equation of mixed type from electron scattering theory
• Indefinite Sturm-Liouville problems and half-range completeness
• Sur une équation d'évolution changeant de type
• Discrete and continuous boundary problems
• Full- and partial-range eigenfunction expansions for Sturm-Liouville problems with indefinite weights
• Albedo operators and H-equations for generalized kinetic models
• Erratum: Partial-range completeness and existence of solutions to two-way diffusion equations [J. Math. Phys. 2 2, 954 (1981)]
• Factorizations of Transfer Functions
• 23.—The Linear Transport Equation. The Degenerate Case c = 1. II. Half-range Theory
• Second-Order Differential Equations with Fractional Transition Points
• Linear analysis and solution of neutron transport problems
• Decompositions of a Hilbert Space and Factorization of a W–A Determinant
• Existence and Uniqueness Theorems for the Neutron Transport Equation
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations

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