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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 1: Variational Analysis, Optimization and Optimal Control. Guest editors: Der-Chen Chang, Robert P. Gilbert, Yongzhi Steve Xu and Jen-Chih Yao
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Articles

On the solvability of implicit differential inclusions

Aram ArutyunovDepartment of Nonlinear Analysis and Optimization, Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow117198, Russia.
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Valeriano Antunes de OliveiraDepartamento de Matematica Aplicada, Instituto de Biociencias, Letras e Ciencias Exatas, UNESP - Univ. Estadual Paulista, Campus de Sao Jose do Rio Preto, São Paulo, Brazil.
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Fernando Lobo PereiraDepartment of Electrical and Computer Engineering, Institute for Systems and Robotics, Universidade do Porto, Rua Dr. Roberto Frias, s/n 4200-465, Porto, Portugal.
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Evgeniy ZhukovskiyDepartment of Algebra and Geometry, Tambov State University, ul. Internatsilonalnaya 33, Tambov392000, Russia.
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Sergey ZhukovskiyDepartment of Electrical and Computer Engineering, Institute for Systems and Robotics, Universidade do Porto, Rua Dr. Roberto Frias, s/n 4200-465, Porto, Portugal.Correspondence[email protected]
Pages 129-143 | Received 09 Oct 2013, Accepted 18 Dec 2013, Published online: 17 Mar 2014
 
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Abstract

In the paper, the set-valued covering mappings are studied. The statements on solvability, solution estimates, and well-posedness of inclusions with conditionally covering mappings are proved. The results obtained are applied to the investigation of differential inclusions unsolved for the unknown function. The statements on solvability, solution estimates, and well-posedness of these inclusions are derived.

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Corrigendum

Acknowledgments

The authors are thankful to Professor V.V. Obukhovskii for the useful remarks and advices.

Notes

This article was originally published with errors. This version has been amended. Please see Corrigendum (http://dx.doi.org/10.1080/00036811.2014.912434)

This work was supported by the Marie Curie International Incoming Fellowship within the seventh European Community Framework Program and by Fundacao de Amparo a Pesquisa do Estado de Sao Paulo - FAPESP [grant number 2013/10272-8].

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