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A Note on the Global Solutions of the Cauchy Problem in Banach Spaces

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Abstract

The aim of this paper is to describe the topological structure of global solutions set of the initial value problem in Banach spaces. More precisely, we prove that under suitable conditions this set is homeomorphic to the intersection of a decreasing sequence of compact absolute retracts (shortly: it is an R 5 set). The main condition in our result is formulated in terms of the Kuratowski measure of noncompactness.

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Authors and Affiliations

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

    Daria Bugajewska

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  1. Daria Bugajewska
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Bugajewska, D. A Note on the Global Solutions of the Cauchy Problem in Banach Spaces. Acta Mathematica Hungarica 88, 341–346 (2000). https://doi.org/10.1023/A:1026736309418

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