This paper deals with the problems of finding periodic solutions for a class of differential equations. Under suitable conditions, we give a constructive proof of the existence of a smooth path connecting the solutions of periodicity problems of differential equations to a given point. Following this path can lead to a globally convergent algorithm. Compared with the previous results in the literature, we can select initial points without satisfying the equality constraints. This point may improve the computational efficiency of the algorithm greatly.

periodicity problems, differential equations, computational efficiency.