Abstract
Existence and asymptotic behavior of solutions are given for the equation u′( t) = − A( t) u( t) + F( t, u t ) ( t ⩾ 0) and u 0 = ϑ ϵ C([− r,0]; X) C. The space X is a Banach space; the family {A(t) ¦ 0 ⩽ t ⩽ T} of unbounded linear operators defined on D( A) ⊂ X → X generates a linear evolution system and F: C → X is continuous with respect to a fractional power of A( t 0) for some t 0 ϵ [0, T].
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