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Zbl 1165.34349
Li, Xiong; Zhang, Ziheng
Periodic solutions for damped differential equations with a weak repulsive singularity.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 6, A, 2395-2399 (2009). ISSN 0362-546X

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 $p, q, c \in L^1(\Bbb R)$ are $T$-periodic functions and $f \in Car(\Bbb R\times \Bbb R^+, \Bbb R)$ 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 2000:
*34C25 Periodic solutions of ODE
47N20 Appl. of operator theory to differential and integral equations

Keywords: positive periodic solutions; weak singularity; Green's function; Schauder's fixed point theorem

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