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We study the existence of a positive periodic solution for second-order singular semipositone differential equation by a nonlinear alternative principle of Leray-Schauder. Truncation plays an important role in the analysis of the uniform positive lower bound for all the solutions of the equation. Recent results in the literature (Chu et al., 2010) are generalized.

We prove the boundedness of all solutions for the equationis of singular potential, i.e., lim x→−1 V (x) = +∞, and G(x, t) is bounded and periodic in t. We give sufficient conditions on V (x) and G(x, t) to ensure that all solutions are bounded.