Abstract: he existence and multiplicity of positive periodic solutions are considered for the secondorder ordinary differential equation u″(t)+k2u(t)=f(t,u(t)), where the nonlinear term f(t,u) may be singular att=0, t=2π and u=0. By constructing suitable control functions and using fixed point theorem on cone, the existence of npositive periodic solutions is proved for the ordinary differential equation, where n is an arbitrarynatural number.

Key words: singular ordinary differential equation, periodic bou ndary value problem, positive solution, existence, multiplicity