Existence of Positive Periodic Solutions for the Liénard Differential Equations with Weakly Repulsive Singularity.

In this paper we discuss the existence of positive T-periodic solutions for the following second order differential equation where f, g:ℝ⁺=(0,+∞)→ℝ are continuous functions, g has a repulsive singularity at the origin and c( t) is a continuous T-periodic function. The novelty of the present article is that for the first time we show that a weakly repulsive singularity enables the achievement of a new existence criterion of positive T-periodic solutions through a basic application of the coincidence degree theory. Recent results in the literature are generalized and significantly improved. [ABSTRACT FROM AUTHOR]