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A remark on Bressan’s regularization theorem

A remark on Bressan’s regularization theorem Differential Equations, Vol. 36, No. 3, 2000, pp. 399-402. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 3, 2000, pp. 355-358. Original Russian Text Copyright Q 2000 by Filippov. ORDINARY DIFFERENTIAL EQUATIONS V. V. Filippov Moscow State University, Russia Received November 4, 1998 Pucci [1] introduced ordinary differential equations with "directionally continuous" right-hand side. A. F. Filippov indicated to me that a similar geometric idea had been used earlier in the studies on equations with discontinuous right-hand side (see [2]). The right-hand side in these equations is discontinuous with respect to the ordinary Euclidean topology. Pucci type equations were studied in a number of papers of the Italian school in theory of ordinary differential equations (e.g., see [3-5]). In particular, equations of this type occur if one uses the selection of a lower semicontinuous right-hand side of a differential inclusion [5]. To clarify the situation, we introduce the following definitions. A cone is a nonempty closed convex subset F C R n satisfying the following conditions: (1) the point Ax belongs to F for any x E F and any positive number ~; (2) F n (-F) = {6}. Let F be a cone in R ", and let Y http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

A remark on Bressan’s regularization theorem

Filippov, V.
Differential Equations , Volume 36 (3) – Nov 15, 2007
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References (4)

Publisher
Springer Journals
Copyright
Copyright © 2000 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/BF02754459
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 36, No. 3, 2000, pp. 399-402. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 3, 2000, pp. 355-358. Original Russian Text Copyright Q 2000 by Filippov. ORDINARY DIFFERENTIAL EQUATIONS V. V. Filippov Moscow State University, Russia Received November 4, 1998 Pucci [1] introduced ordinary differential equations with "directionally continuous" right-hand side. A. F. Filippov indicated to me that a similar geometric idea had been used earlier in the studies on equations with discontinuous right-hand side (see [2]). The right-hand side in these equations is discontinuous with respect to the ordinary Euclidean topology. Pucci type equations were studied in a number of papers of the Italian school in theory of ordinary differential equations (e.g., see [3-5]). In particular, equations of this type occur if one uses the selection of a lower semicontinuous right-hand side of a differential inclusion [5]. To clarify the situation, we introduce the following definitions. A cone is a nonempty closed convex subset F C R n satisfying the following conditions: (1) the point Ax belongs to F for any x E F and any positive number ~; (2) F n (-F) = {6}. Let F be a cone in R ", and let Y

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Differential Equations – Springer Journals

Published: Nov 15, 2007

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