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On a generalization of Krasnoselskii's theorem

Part of: Existence theories Nonlinear operators and their properties Miscellaneous applications of operator theory

Published online by Cambridge University Press:  01 August 2017

Dariusz Idczak  and
Andrzej Rogowski
Dariusz Idczak
Affiliation:
University of Łódź, S.Banacha 22, 90-238 Łódź, Poland e-mail: idczak@math.uni.lodz.pl, arogow@math.uni.lodz.pl
Andrzej Rogowski
Affiliation:
University of Łódź, S.Banacha 22, 90-238 Łódź, Poland e-mail: idczak@math.uni.lodz.pl, arogow@math.uni.lodz.pl
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Abstract

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In this paper we prove a generalization of the well known theorem of Krasnoselskii on the superposition operator in which the domain of Nemytskii's operator is a product space. We also give an application of this result.

Keywords

Nemytskii's operatorvariational methodscontinuous differentiability

MSC classification

Secondary: 49J50: Fréchet and Gateaux differentiability 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) 47N10: Applications in optimization, convex analysis, mathematical programming, economics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 3 , June 2002 , pp. 389 - 394
Copyright
Copyright © Australian Mathematical Society 2002

References

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