Geodesic
Kneser-type theorem for the Darboux problem in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 267-279 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 35L90, 35R20, 46G10
Keywords: Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness 
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     author = {Cicho\'n, Mieczys{\l}aw and Kubiaczyk, Ireneusz},
     title = {Kneser-type theorem for the {Darboux} problem in {Banach} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {267--279},
     year = {2001},
     volume = {42},
     number = {2},
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     zbl = {1115.35141},
     language = {en},
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}
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Cichoń, Mieczysław; Kubiaczyk, Ireneusz. Kneser-type theorem for the Darboux problem in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 267-279. http://geodesic.mathdoc.fr/item/CMUC_2001_42_2_a4/