We consider the Cauchy problem x (t) = f (t,x (t)), x (0) = x0 in a nonreflexive Banach space X and for f: T × X → X a weakly continuous vector field. Using a compactness hypothesis involving a weak measure of noncompactness we prove an existence result that generalizes earlier theorems by Chow-Shur, Kato and Cramer-Lakshmikantham-Mitchell. © 1986, Australian Mathematical Society. All rights reserved.
CITATION STYLE
Papageorgiou, N. S. (1986). Weak solutions of differential equations in Banach spaces. Bulletin of the Australian Mathematical Society, 33(3), 407–418. https://doi.org/10.1017/S0004972700003993
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