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Differential inclusions with unbounded right-hand side: Existence and relaxation theorems

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Abstract

A differential inclusion in which the values of the right-hand side are nonconvex closed possibly unbounded sets is considered in a finite-dimensional space. Existence theorems for solutions and a relaxation theorem are proved. Relaxation theorems for a differential inclusion with bounded right-hand side, as a rule, are proved under the Lipschitz condition. In our paper, in the proof of the relaxation theorem for the differential inclusion, we use the notion of ρ - H Lipschitzness instead of the Lipschitzness of a multivalued mapping.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, Russia

    A. A. Tolstonogov

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  1. A. A. Tolstonogov
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Correspondence to A. A. Tolstonogov.

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Original Russian Text © A. A.Tolstonogov, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 3.

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Tolstonogov, A.A. Differential inclusions with unbounded right-hand side: Existence and relaxation theorems. Proc. Steklov Inst. Math. 291 (Suppl 1), 190–207 (2015). https://doi.org/10.1134/S0081543815090138

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  • DOI: https://doi.org/10.1134/S0081543815090138

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