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Abstract. The paper
is concerned with the existence of almost periodic mild solutions to
evolution equations of the form
ů(t)= Au(t) + f(t) (∗), where A
generates a C-semigroup and f is almost
periodic. We investigate the existence of almost periodic solutions of (∗) by
means of associated implicit difference equations which are well-studied in
recent works on the subject. As results we obtain various sufficient
conditions for the existence of almost periodic solutions to (∗) which
extend previous ones to a more general class of ill-posed equations
involving C-semigroups. The paper is supported by a research grant
of the Vietnam National University,
Hanoi.
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