We study the existence and uniqueness of a positive solution to the problem \({u^{\prime \prime }} = p(t)u + q(t,u)u + f(t);\,\,\,\,\,u(0) = u(\omega ),\,\,\,{u^\prime }(0) = {u^\prime }(\omega )\) with a super-linear nonlinearity and a nontrivial forcing term f. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.
