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ArticleOriginal scientific text

Title

Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

Authors 1, 1

Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Abstract

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 Cw(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.

Keywords

ENG
set of solutions, pseudo-solutions, measures of weak noncompactness, Pettis integral

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Annales Polonici Mathematici
1995/62/1
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Pages:
13-21
Main language of publication
English
Received
1993-06-20
Published
1995
Exact and natural sciences