A Kneser theorem for ordinary differential equations in Banach spaces

Marc Mitschele

Published: 2010-09-30

Vol. 24 (2010)

A Kneser theorem for ordinary differential equations in Banach spaces

Marc Mitschele

Abstract

We show that the set of solutions of the initial-value problem
u(τ)=a, u'(t) = g(t,u(t)) + k(t,u(t)), τ≤t≤T,
in a Banach space is compact and connected, whenever g and k are bounded and continuous functions such that g is one-sided Lipschitz and k is Lipschitz with respect to the Kuratowski measure of noncompactness. The existence of solutions is already known from Sabina Schmidt [10].

Keywords:

ordinary differential equations in Banach spaces , theorem of Sabina Schmidt , theorem of Hellmuth Kneser

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Mitschele, M. (2010). A Kneser theorem for ordinary differential equations in Banach spaces. Annales Mathematicae Silesianae, 24, 71–85. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14036

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References

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Vol. 24 (2010)
Published: 2010-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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