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ArticleOriginal scientific text

Title

Representation of the set of mild solutions to the relaxed semilinear differential inclusion

Authors 1, 2

Affiliations

  1. Dipartimento di Energetica "S. Stecco", University of Florence, Via S. Marta 3, Firenze, Italy
  2. Department of Mathematics, Physics, and Computer Science, Tambov State University, Internazional'naya str. 33, Tambov, Russia

Abstract

We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.

Keywords

ENG
differential inclusion, mild solution, quasi-solution, convexified and perturbed problem, relaxation theorem

Bibliography

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2006/26/1
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Pages:
143-158
Main language of publication
English
Received
2005-11-16
Published
2006

DOI: 10.7151/dmdico.1071

Exact and natural sciences