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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.
47E05 General theory of ordinary differential operators
34K40 Neutral functional-differential equations
34A40 Differential inequalities involving functions of a single real variable