Existence results for neutral functional differential inclusions in Banach algebras. (English) Zbl 1105.34051

The author considers first-order neutral functional-differential inclusions of the form \[ \frac{d}{dt}\left[\frac{x(t)}{(f(t,x(t),x_t)} \right]\in G\left(t,x_t, \int^t_0k(t,s,x_s)\,dt\right). \] A result on the existence of a solution of such inclusions in Banach algebras is obtained under generalized Lipschitz and Carathéodory conditions. The existence of extremal solutions is also established under certain monotonicity conditions.


34K30 Functional-differential equations in abstract spaces
34K40 Neutral functional-differential equations
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