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Estimates for domains of local invertibility of diffeomorphisms

Authors: Octavian G. Mustafa and Yuri V. Rogovchenko
Journal: Proc. Amer. Math. Soc. 135 (2007), 69-75
MSC (2000): Primary 34A12, 57R50
Published electronically: July 28, 2006
MathSciNet review: 2280176
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Abstract: Using a novel Wintner-type formulation of the classical Peano's existence theorem [Math. Ann. 37 (1890), 182-228], we enhance Wazewski's result on invertibility of maps defined on closed balls [Ann. Soc. Pol. Math. 20 (1947), 81-125] securing the size of the domain of invertibility that agrees with the bounds derived by John [Comm. Pure Appl. Math. 21 (1968), 77-110] and Sotomayor [Z. Angew. Math. Phys. 41 (1990), 306-310].

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Octavian G. Mustafa
Affiliation: Department of Mathematics, University of Craiova, Al. I. Cuza 13, Craiova, Romania

Yuri V. Rogovchenko
Affiliation: Department of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, Turkey

Keywords: Nonlinear differential equations, Peano's existence theorem, regularity, diffeomorphism, local invertibility, Wa\.{z}ewski's theorem, Hadamard-L\'evy-Plastock condition
Received by editor(s): June 23, 2005
Published electronically: July 28, 2006
Additional Notes: This research was supported in part by the Mathematisches Forschungsinstitut Oberwolfach, Germany through the Program “Research in Pairs” (O.M. and Y.R.) and by the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, through the Young Collaborators Program (O.M.) and the Associateship Scheme (Y.R.).
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.