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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 3, Pages 246–262
(Mi timm1098)
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This article is cited in 7 scientific papers (total in 7 papers)
Differential inclusions with unbounded right-hand side. Existence and relaxation theorems
A. A. Tolstonogov Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
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 $\rho-H$ Lipschitzness instead of the Lipschitzness of a multivalued mapping.
Keywords:
unbounded differential inclusions, existence and relaxation theorems.
Received: 15.04.2014
Citation:
A. A. Tolstonogov, “Differential inclusions with unbounded right-hand side. Existence and relaxation theorems”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 246–262; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 190–207
Linking options:
https://www.mathnet.ru/eng/timm1098 https://www.mathnet.ru/eng/timm/v20/i3/p246
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