Existence of positive periodic solutions of periodic boundary value problem for second order ordinary differential equations (Q626023)

This paper, through an application of fixed point index theory, establishes a sufficient condition for the existence of positive periodic solutions of the scalar differential equation \[ -x''(t)+b(t)x(t)=g(t)f\big(t,x(t)\big), \] where \(b\) and \(g\) are continuous \(\omega\)-periodic positive real functions and \(f\in C\big({\mathbb R}\times [0,\infty), [0,\infty)\big)\) is \(\omega\)-periodic in the first variable.