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The existence theorem for neutral functional-differential inclusions. (English) Zbl 0762.47017
Introduction: The aim of this paper is to present the existence theorem for functional- differential inclusions of the form
$\frac{d}{dt} D(t,x_t)\in F(t,x_ t),$
where $$F$$ is a multivalued mapping having a Carathéodory selector and taking as its values nonempty closed compact but not necessarily convex or nonempty closed convex subsets of $$R^n$$ and $$D$$ is a single- valued mapping with values in $$R^n$$. We extend the results of J. K. Hale [J. Diff. Equations 9, 168–181 (1971; Zbl 0213.36901)] on the functional-differential inclusions of neutral type.
##### MSC:
 47E05 General theory of ordinary differential operators 34K40 Neutral functional-differential equations 34A40 Differential inequalities involving functions of a single real variable