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On the existence of solutions of differential inclusions in uniformly convex Banach space. (English) Zbl 0831.34013
Summary: This paper deals with the existence of solutions of multivalued differential equations and differential inclusions with delay in uniformly convex Banach spaces. These questions were studied under additional compactness type hypotheses in the existing literature. Here we replace the compactness assumptions with one side Lipschitz condition on the right-hand side. The corresponding approach for the ordinary and functional differential equations is well known. We use the results of V. Lakshmikantham, A. R. Mitchell and R. W. Mitchell [Ann. Pol. Math. 35, 253-260 (1978; Zbl 0373.34034)].

34A60 Ordinary differential inclusions
34G20 Nonlinear differential equations in abstract spaces
34K05 General theory of functional-differential equations