Positive periodic solutions to a generalized Ermakov-Pinney equation with indefinite weights 

We consider a generalized Ermakov-Pinney equation with indefinite weights x" + α(t)x = h(t)/x ρ , where ρ is a real constant and ρ > 0, α, h ∈ L 1 (R/TZ) . Using the positivity of Green'sfunction andKrasnoselskiĭ's-Guo fixed point theorem, we give sufficient conditionsguaranteeing the existence of at least one positive periodicsolution for Ermakov-Pinney equation with indefinite weights. Theresults are applicable to weak as well as strong singularities.