Periodic solutions for second order differential equations with indefinite singularities

In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities x ''(t) + f(x(t))x'(t) + phi(t)x(m)(t) - alpha(t)/x(mu)(t) + beta(t)/x(y)(t) = 0, where f is an element of C((0, +infinity), R) may have a singularity at the origin, the signs of phi and alpha are allowed to change, m is a non-negative constant, it and y are positive constants. The approach is based on a continuation theorem of Manasevich and Mawhin with techniques of a priori estimates.