no. G5
Analyse fonctionnelle, Théorie des opérateurs
On an extension of a global implicit function theorem
Berger, Thomas1  ; Haller, Frédéric2
1 Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany
2 Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany
Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 439-450.

We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible. Generalizing known results, we provide sufficient criteria which are easy to check. These conditions essentially rely on the existence of diffeomorphisms between the respective projections of the set of zeros and appropriate Banach spaces, as well as a corresponding growth bound. The projections further allow to consider cases where the global implicit function is not defined on all of the open subset corresponding to the first variable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.309
Classification : 26B10, 58C15
Berger, Thomas 1 ; Haller, Frédéric 2

1 Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany
2 Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany 
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Berger, Thomas; Haller, Frédéric. On an extension of a global implicit function theorem. Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 439-450. doi : 10.5802/crmath.309. http://www.numdam.org/articles/10.5802/crmath.309/

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