Retarded functional differential equations with nondense domain operators (Q1817771)

The uniqueness of an \textit{integral solution} and of a \textit{solution} to the abstract retarded Cauchy problem \[ x'(t)=Bx(t)+Lx_t, t\geq 0,\quad x_0=\varphi, \] where \(B\) is a~nondensely defined closed linear operator on a~Banach space \(X\) and \(L\) is a~bounded linear operator from \(C:=C([-r,0];X)\), \(r>0\) to \(X\), is studied. Results concerning the existence of a~unique \textit{integral solution} or \textit{solution} are proved as well as results concerning properties of the operator \(A\) which corresponds to the problem considered. An illustrative example is discussed.