We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007) . In some suitable weak singularities, the existence of periodic solutions may help.
"Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations." J. Appl. Math. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/575204