A periodic boundary value problem with vanishing Green’s function

In this work, the authors consider the boundary value problem {y″+a(t)y=g(t)f(y),0≤t≤2π,y(0)=y(2π),y′(0)=y′(2π), and establish the existence of nonnegative solutions in the case where the associated Green’s function may have zeros. The results are illustrated with an example.