A continuous version of the Filippov-Gronwall inequality for differential inclusions
Ornelas, António
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 1 (1990), p. 105-110 / Harvested from Biblioteca Digitale Italiana di Matematica
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We give an estimate for the distance between a given approximate solution for a Lipschitz differential inclusion and a true solution, both depending continuously on initial data.

Si determina una stima per la distanza fra una data soluzione approssimata di una inclusione differenziale lipschitziana e una vera soluzione, con dipendenza continua dai dati iniziali.

Publié le : 1990-05-01
@article{RLIN_1990_9_1_2_105_0,
     author = {Ant\'onio Ornelas},
     title = {A continuous version of the Filippov-Gronwall inequality for differential inclusions},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {1},
     year = {1990},
     pages = {105-110},
     zbl = {0719.34032},
     mrnumber = {1081392},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1990_9_1_2_105_0}
}

Ornelas, António. A continuous version of the Filippov-Gronwall inequality for differential inclusions. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 1 (1990) pp. 105-110. http://gdmltest.u-ga.fr/item/RLIN_1990_9_1_2_105_0/

[1] Antosiewicz, H. A. - Cellina, A., Continuous selections and differential relations. J. Diff. Eq., 19, 1975, 386-398. | MR 430368 | Zbl 0279.54007

[2] Aubin, J. P. - Cellina, A., Differential inclusions. Springer, New York 1984. | MR 755330 | Zbl 0538.34007

[3] Cellina, A., On the set of solutions to lipschitzian differential inclusions. Diff. and Integral Eq., to appear. | MR 945823 | Zbl 0723.34009

[4] Cellina, A. - Ornelas, A., Representation of the attainable set for lipschitzian differential inclusions. Preprint SISSA, 73 M, 1988. | MR 1159946 | Zbl 0752.34012

[5] Filippov, A. F., Classical solutions of differential equations with multivalued right hand side. Vestnik, Moskov. Univ. Ser. Mat. Mech. Astr.22, 1967, 16-26. [english translation: SIAM J. Controls, 1967, 609-621]. | MR 220995 | Zbl 0238.34010

[6] Fryszkowski, A., Continuous selections for a class of nonconvex multivalued maps. Studia Math., 76, 1983, 163-174. | MR 730018 | Zbl 0534.28003

[7] Himmelberg, C. J., Measurable relations. Fund. Math., 87, 1975, 53-72. | MR 367142 | Zbl 0296.28003

[8] Himmelberg, C. J. - Van Vleck, F. S., Lipschitzian generalized differential equations. Rend Sem. Mat. Padova, 48, 1972, 159-169. | MR 340692 | Zbl 0289.49009