We study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu″+λa(t)g(u)=0,λ>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

%B Journal of Differential Equations %V 252 %P 2900 - 2921 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039611003895 %R https://doi.org/10.1016/j.jde.2011.09.011