Discussiones Mathematicae Differential Inclusions 19 (1999) 111-121

Mouffak Benchohra

*Département de Mathématiques, Université de Sidi Bel Abbes
BP 89, 22000 Sidi Bel Abbes, Algérie*

In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.

**Key words and phrases:** initial value problems, convex multivalued map, mild
solution, evolution inclusion, existence, fixed point, abstract space.

**1991 Mathematics Subject Classifications:** 34A60, 34G20.

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Received 12 August 1999