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Kneser's theorem for differential equations in Banach spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
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 .
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- Copyright © Australian Mathematical Society 1986
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