Two-Dimensional Coulomb Dynamics of Two and Three Equal Negative Charges in the Field of Two Equal Fixed Positive Charges

We find periodic and bounded (for positive time) solutions of the planar Coulomb equations of motion for two and three identical negative charges in the field of two equal fixed positive charges. The analyzed systems have equilibrium configurations and the constructed bounded solutions converge to these configurations in the infinite-time limit. The periodic solutions are obtained with the help of the Lyapunov center theorem.