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Existence of solutions for a class of nonconvex differential inclusions

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Existence of solutions for a class of nonconvex differential inclusions RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA F. ANCONA G. COLOMBO Existence of solutions for a class of nonconvex differential inclusions Rendiconti del Seminario Matematico della Università di Padova, tome 83 (1990), p. 71-76. <http://www.numdam.org/item?id=RSMUP_1990__83__71_0> © Rendiconti del Seminario Matematico della Università di Padova, 1990, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’ac- cord avec les conditions générales d’utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Existence of Solutions for a Class of Nonconvex Differential Inclusions. F. ANCONA - G. COLOMBO (*) SUMMARY - We prove existence of solutions for the Cauchy problem where F is upper semicontinuous and F(x) is contained in the subdiffer- ential i)V(x) of a convex continuous function V, while f is a Carathéodory single valued map. 1. Introduction. It is well known that the initial value problem for the differentiql inclusion x E may not have solutions when F is upper semi- continuous but has not necessarily convex values. Bressan, Cellina and Colombo have recently [2] given a condition ensuring existence for the Cauchy problem They assume F to be upper semicontinuous with values contained in the subdifferential 8V of a convex function TT: This func- tion permits to estimate the .L2-norm of the derivatives of approximat- (*) Indirizzo degli AA. : F. ANCONA: Via Trieste 1 - 35100 Padova (Italy); G. COLOMBO: S.I.S.S.A., Strada Costiera 11 - 34014 Trieste (Italy). 72

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