Abstract
For (scalar) nonlinear two-point boundary value problems of the form−U ″+F(x, U, U′)=0, B 0 [U]=B 1 [U]=0, with Sturm-Liouville or periodic boundary operatorsB 0 andB 1, we present a method for proving the existence of a solution within a “close”C 1-neighborhood of an approximate solution.
Zusammenfassung
Für (skalare) nichtlineare Zweipunkt-Randwertprobleme der Form−U ″+F(x, U, U′)=0,B 0 [U]=B 1 [U]=0 mit Sturm-Liouville-oder periodischen RandoperatorenB 0,B 1 wird eine Methode vorgestellt, mit der die Existenz einer Lösung innerhalb einer “kleinen”C 1-Umgebung einer Näherungslösung bewiesen werden kann.
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Plum, M. Computer-assisted existence proofs for two-point boundary value problems. Computing 46, 19–34 (1991). https://doi.org/10.1007/BF02239009
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DOI: https://doi.org/10.1007/BF02239009