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Zbl 0851.34014
Hu, Shouchuan; Papageorgiou, Nikolaos S.
On the existence of periodic solutions for nonconvex-valued differential inclusions in $\bbfR\sp N$.
(English)
[J] Proc. Am. Math. Soc. 123, No.10, 3043-3050 (1995). ISSN 0002-9939; ISSN 1088-6826/e

This paper deals with the multivalued periodic problem $x'\in F(t, x(t))$, $x(0)= x(b)$, where $F: [0, b]\times \bbfR^n\to \bbfR^n$ is a set-valued function with closed (not necessary convex 0) values, measurable with respect to both variables and lower semicontinuous with respect to the second variable. Using a tangential condition and directional selectors the authors establish the existence of periodic solutions. It is worth to note that on that occasion they prove a useful version of the Scorza-Dragoni property for lower semicontinuous multifunctions and they also study the lower semicontinuity of the intersection of two multifunctions.
[J.Myjak (L'Aquila)]
MSC 2000:
*34A60 ODE with multivalued right-hand sides
34C25 Periodic solutions of ODE

Keywords: differential inclusion; multivalued periodic problem; directional selectors; periodic solutions; Scorza-Dragoni property; lower semicontinuous multifunctions

Cited in: Zbl 0981.34026 Zbl 0939.34013

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