Geodesic
Kneser-type theorem for the Darboux problem in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 267-279

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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.
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},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2001},
     mrnumber = {1832146},
     zbl = {1115.35141},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001__42_2_a4/}
}
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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/