Periodic solutions for damped differential equations with a weak repulsive singularity

This paper deals with the existence of positive TT-periodic solutions for the following damped differential equation ẍ+p(t)ẋ+q(t)x=f(t,x)+c(t), where pp, qq, c∈L1(R)c∈L1(R) are TT-periodic functions and f∈Car(R×R+,R) is TT-periodic in the first variable. We will prove that a weak repulsive singularity enables the achievement of new existence criteria through a basic application of Schauder’s fixed point Theorem.