On the solvability of implicit differential inclusions

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.

Keywords:

• conditionally covering mapping
• Lipschitz perturbation
• implicit differential inclusion

AMS Subject Classifications:

• 47J22
• 34A60

View correction statement:

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].