Periodic solutions for damped differential equations with a weak repulsive singularity

Abstract

This paper deals with the existence of positive T -periodic solutions for the following damped differential equation x ̈ + p ( t ) x ̇ + q ( t ) x = f ( t , x ) + c ( t ) , where p , q , c ∈ L 1 ( R ) are T -periodic functions and f ∈ Car ( R × R + , R ) is T -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.