The authors focus on three fixed point theorems and an integral equation. Schaefer’s fixed point theorem yields a -periodic solution of
if and satisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder’s theorem (known as Krasnoselskii’s theorem) yields a -periodic solution of
if defines a contraction and if and are small enough.
The authors prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer’s theorem which yields a -periodic solution of (2) when defines a contraction mapping, while and satisfy the aforementioned sign conditions.