Mieczys\l aw Cicho\'n, Ireneusz Kubiaczyk
Kneser-type theorem for the Darboux problem in Banach spaces

Comment.Math.Univ.Carolinae 42,2 (2001) 267-279.

Abstract:In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

Keywords: Pettis integral, Fubini theorem, Darboux problem, measure of weak noncompactness
AMS Subject Classification: 35R20, 46G10