Problems of group pursuit with equal opportunities in a presence of defenders for an evader

The necessary and sufficient conditions for multiple capture in the group pursuit problems with equal opportunities in the presence of a group of defenders for an evader are obtained. Capture means a coincidence of geometric coordinates for the evader and the pursuer if the latter up to the moment of capture was possible to avoid a meeting with all the defenders of the evader. Multiple capture occurs when a given number of pursuers catch an evader and the moments of capture may not coincide. In the nonstrict simultaneous multiple capture problem, one needs a coincidence of capture times.