Applications of Schauder's fixed point theorem to semipositone singular differential equations (Q2336552)

Summary: 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 \textit{J. Chu} and \textit{P. J. Torres} [Bull. Lond. Math. Soc. 39, No. 4, 653--660 (2007; Zbl 1128.34027)] and \textit{P. J. Torres} [J. Differ. Equations 232, No. 1, 277--284 (2007; Zbl 1116.34036)]. In some suitable weak singularities, the existence of periodic solutions may help.