On a global diffeomorphism between two Banach spaces and some application

Marek Galewski; Marcin Koniorczyk

doi:10.1556/sscmath.52.2015.1.1302

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 52: Issue 1

On a global diffeomorphism between two Banach spaces and some application

Authors:

Marek Galewski

Marek Galewski Technical University of Lodz Institute of Mathematics Wolczanska 215 90-924 Lodz Poland

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Marcin Koniorczyk

Marcin Koniorczyk Technical University of Lodz Institute of Mathematics Wolczanska 215 90-924 Lodz Poland

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Pages:: 65–86

Online Publication Date:: 17 Mar 2015

Publication Date:: 01 Mar 2015

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.52.2015.1.1302

Keywords:: Primary 57R50; 58E05; global diffeomorphism; local diffeomorphism; mountain pass lemma; integro-differential equation

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We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism. We get local diffeomorhism by standard method while in making it global we employ a critical point theory and a duality mapping. We provide application to integro-differential initial value problem for which we get differentiable dependence on parameters.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language	English French German
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ISSN	0081-6906 (Print)
ISSN	1588-2896 (Online)