Remarks 1, 3 and 5 are incorrect as stated. They should be supplemented by the following observations:

(i) In case the perturbing term is linear in y, i.e. f(t, y) = B(t)y, the conclusion of Theorem 1 will follow from Lemma 1 when applied to equation (15) if we assume, instead of (6),

The hypothesis given in Trench's theorem is sufficient to imply (*) but not (6). A similar comment applies to Remark 5.