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differential inclusion; relaxation property; tangent cone
A certain converse statement of the Filippov-Wa\v zewski theorem is proved. This result extends to the case of time dependent differential inclusions a previous result of Jo'o and Tallos in [5] obtained for autonomous differential inclusions.
[1] Aubin J.P., Cellina A.: Differential Inclusions. Springer, Berlin, 1984. MR 0755330 | Zbl 0538.34007
[2] Aubin J.P., Frankowska H.: Set-valued Analysis. Birkhäuser, Basel, Boston, 1989. MR 1048347 | Zbl 1168.49014
[3] Frankowska H.: Local controllability and infinitesimal generators of semi-groups of set-valued maps. SIAM J. Control Optim. 25 (1987), 412-431. MR 0877070
[4] Frankowska H.: Control of Nonlinear Systems and Differential Inclusions. Birkhäuser, to appear.
[5] Joó I., Tallos P.: The Filippov-Wažewski Relaxation Theorem revisited. Acta Math. Hungar. 83 (1999), 171-177. MR 1682910
[6] Zhu Q.J.: On the solution set of differential inclusions in Banach space. J. Differential Equations 93 (1991), 213-237. MR 1125218 | Zbl 0735.34017
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