A Kneser theorem for ordinary differential equations in Banach spaces



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≤tT,
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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Published : 2010-09-30


MitscheleM. (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

Marc Mitschele  marc.mitschele@kit.edu
Institut für Analysis, Karlsruher Institut für Technologie, Germany  Germany



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