Periodic solutions of Liénard equation with a singularity and a deviating argument

In this paper, we study the existence of periodic solutions of the Liénard equation with a singularity and a deviating argument x″+f(x)x′+g(t,x(t−σ))=0.x″+f(x)x′+g(t,x(t−σ))=0. When gg has a strong singularity at x=0x=0 and satisfies a new small force condition at x=∞x=∞, we prove that the given equation has at least one positive TT-periodic solution.