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On the solution sets to differential inclusions on an unbounded interval

Published online by Cambridge University Press:  20 January 2009

Vasile Staicu
Vasile Staicu
Affiliation:
Department of Mathematics, Aveiro University, 3810–193 Aveiro, Portugal (vasile@mat.ua.pt)
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Abstract

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We prove that for F: [0,∞) × ℝn → K (ℝn) a Lipschitzian multifunction with compact values, the set of derivatives of solutions of the Cauchy problem

is a retract of

Keywords

Lipschitzian differential inclusionsolution setderivatives of solutionsabsolute retract

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 475 - 484
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

1.Aubin, J. P. and Cellina, A., Differential inclusions (Springer, Berlin, 1984).Google Scholar
2.Bressan, A., Cellina, A. and Fryszkowski, A., A class of absolute retracts in space of integrable functions, Proc. Am. Math. Soc. 112 (1991), 413–418.CrossRefGoogle Scholar
3.Bressan, A. and Colombo, G., Extensions and selections of maps with decomposable values, Studia Math. 102 (1992), 209–216.CrossRefGoogle Scholar
4.Bressan, A. and Crasta, G., Extremal selections of multifunctions generating a continuous flow, Ann. Polon. Math. 40 (1994), 101–117.Google Scholar
5.Colombo, R., Fryszkowski, A., Rzezukowski, T. and Staicu, V., Continuous selections of solution sets of lipschitzian differential inclusions. Funkcial. Ekvac. 34 (1991), 321–330.Google Scholar
6.De Blasi, F. S. and Pianigiani, G., On the solution sets of nonconvex differential inclusions, J. Diff. Eqns 128 (1996), 541–555.CrossRefGoogle Scholar
7.De Blasi, F. S.Pianigiani, G. and Staicu, V., Topological properties of nonconvex differential inclusions of evolution type, Nonlinear Analysis 24 (1995), 711–720.Google Scholar
8.Gorniewicz, L., On the solution sets of differential inclusions, J. Math. Analysis Appl. 113 (1986), 235–244.CrossRefGoogle Scholar
9.Hiai, F. and Umegaki, H., Integrals, conditional expectations and martingales of multivalued maps, J. Multivariate Analysis 7 (1977), 149–182.Google Scholar
10.Naselli Ricceri, O. and Ricceri, B., Differential inclusions depending on a parameter, Bull. Pol. Acad. Sci. 37 (1989), 665–671.Google Scholar
11.Papagiorgiou, N. S., A property of the solution set of differential inclusions in Banach spaces with Carathéodory orienter, Applic. Analysis 27 (1988), 279–286.CrossRefGoogle Scholar
12.Ricceri, B., Une proprieté topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes, Rend. Accad. Naz. Lincei 81 (1987), 283–286.Google Scholar
13.Staicu, V., Arcwise connectedness of solution sets to differential inclusions, technical report CM/I 41 (Aveiro University, 1998)Google Scholar
14.Tolstonogov, A. A., On the structure of the solution sets for differential inclusions in Banach spaces, .Mat. USSR Sb. 46 (1983), 1–15.Google Scholar