## 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.

### MSC:

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

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