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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
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