We consider a generalized Ermakov–Pinney equation with indefinite weights \(\begin{aligned} x''+a(t)x=\frac{h(t)}{x^\rho }, \end{aligned}\) where \(\rho \) is a real constant and \(\rho >0\) , \(a,~h\in L^\infty (\mathbb {R}/T\mathbb {Z})\) . Using the positivity of Green’s function and Krasnoselski \(\breve{\text{ i }}\) ’s–Guo fixed point theorem, we give sufficient conditions guaranteeing the existence of at least one positive periodic solution for Ermakov–Pinney equation with indefinite weights. The results are applicable to weak as well as strong singularities.
