Electron. J. Diff. Equ., Vol. 2014 (2014), No. 99, pp. 1-6.

Conditions for having a diffeomorphism between two Banach spaces

Marek Galewski, Elzbieta Galewska, Ewa Schmeidel

We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism. Standart arguments allow us to obtain a local diffeomorphism. It is proved to be global using mountain pass geometry.

Submitted February 19, 2014. Published April 11, 2014.
Math Subject Classifications: 57R50, 58E05.
Key Words: Global diffeomorphism; local diffeomorphism; mountain pass lemma.

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Marek Galewski
Institute of Mathematics, Lodz University of Technology
Wolczanska 215, 90--924 Lodz, Poland
email: marek.galewski@p.lodz.pl
  Elzbieta Galewska
Centre of Mathematics and Physics, Lodz University of Technology
al. Politechniki 11, 90--924 Lodz, Poland
email: elzbieta.galewska@p.lodz.pl
Ewa Schmeidel
Faculty of Mathematics and Computer Science
University of Bialystok
Akademicka 2, 15--267 Bialystok, Poland
email: eschmeidel@math.uwb.edu.pl

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