Evasion differential game of multiple pursuers and a single evader with geometric constraints in L2

We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in ℓ2. The control functions of the players are subject to geometric constraints. The pursuers' goal is to bring the state of at least one of the controlled systems to the origin of ℓ2, while the evader's goal is to prevent this from happening in a finite interval of time. We derive a sufficient condition for evasion from any initial state and construct an evasion strategy for the evader.