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Kneser's theorem for differential equations in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Nikolaos S. Papageorgiou
Nikolaos S. Papageorgiou
Affiliation:
Department of Mathematics, University of Illinois, 1409 W. Green st., Urbana, Illinois 61801, U. S. A.
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Abstract

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We consider the Cauchy problem x (t) = f (t,x (t)), x (O) = xO defined in a nonreflexive Banach space and with the vector field f: T × X → X being weakly uniformly continuous. Using a compactness hypothesis that involves the weak measure of noncompactness, we prove that the solution set of the above Cauchy problem is nonempty, connected and compact in .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 419 - 434
Copyright
Copyright © Australian Mathematical Society 1986

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