Differential Game of Two Pursuers Chasing One Evader with Different Forms of Constraints in l_2- Space

This paper addresses a pursuit differential game involving two Pursuers chasing one Evader within the l2 -space for an infinite system of first-order differential equations. The first Pursuer employs a strategy that satisfied integral constraint, while the second Pursuer uses a strategy governed by a geometric constraint. The goal of each pursuer is to force the state of the system to coincide with a predefined state within a finite time, counteracting the Evader's opposing actions. We construct an explicit strategy to determine the conditions necessary for successful pursuit. Moreover, we explore a control problem involving a single player.