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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 753–760
DOI: 10.4171/ZAA/1106

Published online: 2002-09-30

A Leray-Schauder Alternative for Mönch Maps on Closed Subsets of Fréchet Spaces

Marlène Frigon[1] and Donal O'Regan[2]

(1) Université de Montréal, Canada
(2) National University of Ireland, Galway, Ireland

In this paper, a continuation principle is obtained for maps defined on a closed, convex subset which may have empty interior in a Fréchet space, and satisfying a condition of Mönch type. An application to first order systems of differential equations is presented to illustrate our theory.

Keywords: Fixed points, Mönch maps, Leray-Schauder alternatives

Frigon Marlène, O'Regan Donal: A Leray-Schauder Alternative for Mönch Maps on Closed Subsets of Fréchet Spaces. Z. Anal. Anwend. 21 (2002), 753-760. doi: 10.4171/ZAA/1106