The spatial Hill lunar problem: periodic solutions emerging from equilibria

In this paper, we provide sufficient conditions for the existence of periodic solutions emerging of the equilibrium points of the spatial Hill lunar problem having the following equations of motion: d(2)x/dt(2) - 2dy/dt - 9x = epsilon F-1 (t, x, dx/dt, y, dy/dt), d(2)y/dt(2) + 2dx/ dt + 3y = epsilon F-2 (t, x, dx/ dt, y, dy/dt), d(2)z/dt(2) + 4z = epsilon F-3 (t, x, dx/dt, y, dy/dt). E is a small parameter and F-i, i {1, 2, 3}, are smooth periodic functions in t which define a perturbation in resonance p:q with some of the periodic solutions of the spatial Hill lunar problem being p and q positive relatively prime integers.