  Nonlinear differential equations are derived that describe the time evolution
of the test particle coordinates during finite motions in the gravitational
field of oscillating dark matter. It is shown that in the weak field
approximation, the radial oscillations of a test particle and oscillations in
orbital motion are described by the Hill equation and the nonhomogeneous Hill
equation, respectively. In the case of scalar dark matter with a logarithmic
self-interactions, these equations are integrated numerically, and the
solutions are compared with the corresponding solutions of the original
nonlinear system to identify possible resonance effects.
