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2018 Schauder's Theorem and the method of a priori bounds
Andrzej Granas, Marlene Frigon
Topol. Methods Nonlinear Anal. 52(1): 99-109 (2018). DOI: 10.12775/TMNA.2017.053

Abstract

We first recall simple proofs relying on the Schauder Fixed Point Theorem of the Nonlinear Alternative, the Leray-Schauder Alternative and the Coincidence Alternative for compact maps on normed spaces. We present also an alternative for compact maps defined on convex subsets of normed spaces. Those alternatives permit to apply the method of a priori bounds to obtain results establishing the existence of solutions to differential equations. Using those alternatives, we present some new proofs of existence results for first order differential equations.

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Andrzej Granas. Marlene Frigon. "Schauder's Theorem and the method of a priori bounds." Topol. Methods Nonlinear Anal. 52 (1) 99 - 109, 2018. https://doi.org/10.12775/TMNA.2017.053

Information

Published: 2018
First available in Project Euclid: 24 April 2018

zbMATH: 07029863
MathSciNet: MR3867981
Digital Object Identifier: 10.12775/TMNA.2017.053

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 1 • 2018
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