### Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (2001)

Commentationes Mathematicae Universitatis Carolinae

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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.