Two nonlinear days in Urbino 2017. Electron. J. Diff. Eqns., Conference 25 (2018), pp. 87-102.

Global invertibility of mappings between Banach spaces and applications to nonlinear equations

Marek Galewski, Dusan Repovs

We provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify and generalize our previous results. Applications to algebraic equations and to integro-differential systems are also given.

Published September 15, 2018.
Math Subject Classifications: 57R50, 58E05.
Key Words: Global diffeomorphism; local diffeomorphism; algebraic equation; mountain pass lemma; integro-differential system.

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Marek Galewski
Institute of Mathematics
Lodz University of Technology
Wolczanska 215, 90-024 Lodz, Poland
Dusan Repovs
Faculty of Education and
Faculty of Mathematics and Physics
University of Ljubljana
SI-1000, Slovenia

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