Abstract: | For a sectorial operator A with spectrum (A) that acts in a complex Banach space B, we prove that the condition (A) i
R = Ø is sufficient for the differential equation
where is a small positive parameter, to have a unique bounded solution x
for an arbitrary bounded function f: R B that satisfies a certain Hölder condition. We also establish that bounded solutions of these equations converge uniformly on R as 0+ to the unique bounded solution of the differential equation x(t) = Ax(t) + f(t). |