This paper deals with a scalar second order equation of the form
where satisfies a variant of the Carathéodory conditions; moreover, a sublinear condition of the form is assumed, where and . The first result deals with the periodic boundary value problem associated to the given equation. Assuming (setting ) that , the existence of at least one -periodic solution is proved.
In the second result, the periodic boundary condition is replaced by the impulsive condition , where and the impulse functions are continuous for all . Besides the same assumptions on considered in the first result, it is assumed that, for some and , one has and for all . Under these hypotheses, the existence of at least one -periodic solution is proved. The proofs are performed by applying the saddle point theorem.