The evolution operator approach to functional-differential equations with delay

Ruess, Wolfgang M.

doi:10.1090/S0002-9939-1993-1154248-8

The evolution operator approach to functional-differential equations with delay
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by Wolfgang M. Ruess

Proc. Amer. Math. Soc. 119 (1993), 783-791

DOI: https://doi.org/10.1090/S0002-9939-1993-1154248-8

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Abstract:

The nonlinear nonautonomous functional differential equation $\dot x(t) \in B(t) x(t) + F(t,{x_t}),\;t \geqslant s, {x_s} = \varphi$, is considered. The representation of the solution to this equation via the associated evolution operator is extended from the single-valued case to the general case of multivalued operators $B(t)$.

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