Lower semicontinuous differential inclusions. One-sided Lipschitz approach

• Autorzy: Tzanko Donchev
• Języki publikacji: EN

Abstrakty

EN

Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 74
• Numer: 2
• Strony: 177-184

Daty

wydano

1998

otrzymano

1996-08-07

Twórcy

autor

Tzanko Donchev

• Department of Mathematics, University of Mining and Geology, 1100 Sofia, Bulgaria

Bibliografia

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• [3] D K. Deimling, Multivalued Differential Equations, de Gruyter, Berlin, 1992.
• [4] T. Donchev, Functional differential inclusions with monotone right-hand side, Nonlinear Anal. 16 (1991), 533-542.
• [5] T. Donchev and R. Ivanov, On the existence of solutions of differential inclusions in uniformly convex Banach spaces, Mat. Balkanica 6 (1992), 13-24.
• [6] V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon, 1981.
• [7] P N. Papageorgiou, A relaxation theorem for differential inclusions in Banach space, Tôhoku Math. J. 39 (1987), 505-517.
• [8] A. Pliś, On trajectories of orientor fields, Bull. Acad. Polon. Sci. 13 (1965), 571-573.
• [9] T A. Tolstonogov, Differential Inclusions in Banach Spaces, Novosibirsk, 1986 (in Russian).
• [10] V V. Veliov, Differential inclusions with stable subinclusions, Nonlinear Anal. 23 (1994), 1027-1038.