Geodesic
Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces
Annales Polonici Mathematici, Tome 62 (1995) no. 1, pp. 13-21.

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We investigate the structure of the set of solutions of the Cauchy problem x' = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in $C_{w}(I,E)$, the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory solutions, so we also obtain Kneser-type theorems for these classes of solutions.
DOI : 10.4064/ap-62-1-13-21
Keywords: set of solutions, pseudo-solutions, measures of weak noncompactness, Pettis integral

Mieczysław Cichoń 1 ; Ireneusz Kubiaczyk 1

1 
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Mieczysław Cichoń; Ireneusz Kubiaczyk. Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces. Annales Polonici Mathematici, Tome 62 (1995) no. 1, pp. 13-21. doi : 10.4064/ap-62-1-13-21. http://geodesic.mathdoc.fr/articles/10.4064/ap-62-1-13-21/

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