Periodic solutions for Liénard equation with an indefinite singularity (Q1729181)

The authors study the existence of positive periodic solutions for a scalar equation of the type \[ x''(t)+f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}=0. \] Here, the function \(f\) may have a singularity at the origin, and the signs of the \(T\)-periodic functions \(\varphi(t)\) and \(\alpha(t)\) are allowed to change. They prove some existence results by the use of continuation theory, under some technical assumptions, thus partly solving a problem raised by Hakl, Torres and Zamora.