Abstract
In this paper we consider a certain multipoint-boundary-value-problem and a related eigenvalue-problem the solutions of which are allowed to have spline-character. A representation of the corresponding Green’s function as a spline-interpolation error is derived. If the underlying differential operator is disconjugate this representation leads to the controllability of the sign-structure of the Green’s function. Making use of this result within the theory of partially ordered Banach spaces we get the existence of an eigenvalue of the eigenvalue-problem as well as upper and lower bounds for it.
Diese Arbeit enthält Teile meiner Dissertation [7], die unter der Anleitung von Prof. Dr. E. Bohl an der Universität Münster entstand.
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Literaturverzeichnis
Bohl, E.: Monotonie: Lösbarkeit und Numerik bei Operatorgleichungen. Berlin-Heidelberg-New York, Springer-Verlag 1974.
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Mackens, W.: Untersuchungen Greenscher Funktionen zu Spline-Randwertaufgaben. Dissertation. Münster 1976.
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Mackens, W. (1977). Ein Quotienteneinschluss bei Spline-Eigenwertaufgaben. In: Bohl, E., Collatz, L., Hadeler, K.P. (eds) Numerik und Anwendungen von Eigenwertaufgaben und Verzweigungsproblemen. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’analyse Numérique, vol 38. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5579-2_3
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DOI: https://doi.org/10.1007/978-3-0348-5579-2_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-0938-1
Online ISBN: 978-3-0348-5579-2
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