The aim of this paper is to investigate sufficient conditions (Theorem 1) for the nonexistence of nontrivial periodic solutions
of equation (1.1) withp ≡ 0 and (Theorem 2) for the existence of periodic solutions of equation (1.1).
wheree1 ande2 are real constants ande1 ande2 are not both zero. They proved that there are no non-trivial periodic solutions except possibly for the case
. They left that case as an open problem. In this note we prove that there are indeed no non-trivial periodic solutions in the case
either. Our method of proof consists essentially of constructing a Dulac function (see  and ) and using the conception of Duff's rotated vector field (see , , , , and ).