A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type

摘要

In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type x^″(t) + f(x(t))x^′(t)−g(x(t)) + φ(t)x(t) = h(t),  where g(x) is singular at x = 0, φ and h are T-periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained. It is interesting that the sign of the function φ(t) is allowed to change for t ∈ [0, T].