Extrapolation and inhomogeneous retarded differential equations on infinite dimensional spaces
The authors study linear delay equations \[ \dot x(t) = Bx(t) + Lx_t + f(t),\quad x_0 = f \in C([-r,0],X), \] where \(X\) is a Banach space, \(B\) the generator of a strongly continuous semigroup on \(X\) and \(L\) a bounded linear operator from \(C([-r,0],X)\) into \(X\). Using extrapolation spaces they obtain, via an extrapolated semigroup on \(X \times C([-r,0],X)\) and the corresponding variation of parameters formula, unique mild solutions to the above problem.
scientific article; zbMATH DE number 1203701