Abstract
In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities
$$\begin{array}{}
\displaystyle
x''(t)+ f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}+\frac{\beta(t)}{x^y (t)}=0,
\end{array}$$
where f ∈ C((0, +∞), ℝ) may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, μ and y are positive constants. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates.