## Periodic solutions for damped differential equations with a weak repulsive singularity.(English)Zbl 1165.34349

Summary: This paper deals with the existence of positive $$T$$-periodic solutions for the damped differential equation
$\ddot x +p(t)\dot x+q(t)x = f(t,x)+c(t)$
where $$p, q, c \in L^1(\mathbb R)$$ are $$T$$-periodic functions and $$f \in Car(\mathbb R\times \mathbb R^+, \mathbb R)$$ 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.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
Full Text:

### References:

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