We study the finite delay evolution equation
{x'(t)=Ax(t)+F(t,xt), t≥0,x0=ϕ∈C([−r,0],E),
where the linear operator A
is non-densely defined and satisfies the Hille-Yosida
condition. First, we obtain some properties of integral solutions for this case
and prove the compactness of an operator determined by integral solutions. This
allows us to apply Horn's fixed point theorem to prove the existence of periodic
integral solutions when integral solutions are bounded and ultimately bounded.
This extends the study of periodic solutions for densely defined operators to the
non-densely defined operators. An example is given.