On a certain converse statement of the Filippov-Wažewski relaxation theorem
نویسنده
چکیده
A certain converse statement of the Filippov-Wažewski theorem is proved. This result extends to the case of time dependent differential inclusions a previous result of Joó and Tallos in [5] obtained for autonomous differential inclusions.
منابع مشابه
On the theorem of Filippov – Pliś and some applications
In the paper some known and new extensions of the famous theorem of Filippov (1967) and a theorem of Pliś (1965) for differential inclusions are presented. We replace the Lipschitz condition on the set-valued map in the right-hand side by a weaker onesided Lipschitz (OSL), one-sided Kamke (OSK) or a continuity-like condition (CLC). We prove new Filippov-type theorems for singularly perturbed an...
متن کاملA relaxation theorem for a differential inclusion with ”maxima”
We consider a Cauchy problem associated to a nonconvex differential inclusion with ”maxima” and we prove a Filippov type existence result. This result allows to obtain a relaxation theorem for the problem considered.
متن کاملSome Results on Baer's Theorem
Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.
متن کاملAn Infinite-time Relaxation Theorem for Differential Inclusions
The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wažewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial ...
متن کاملThe Converse of the Theorem concerning the Division of a Plane by an Open Curve*
In his paper, "On the foundations of plane analysis situs,"\ R. L. Moore proved that if I is an open curve % and S is the set of all points, then S — I = Si + Si, where Si and Si are connected point sets such that every arc from a point of Si to a point of Si contains at least one point of ¿.§ Clearly the sets Si and £2 are non-compact. || Professor Moore's theorem is proved on the basis of his...
متن کامل