Pursuit Differential Game Problems of L-Catch in A Hilbert Space

We propose some fixed duration pursuit differential game problems of l-catch in a Hilbert space. Players' motions obey ordinary differential equations and the control functions of players are subjected to either integral or geometric constraints. Pursuit is said to be completed in l-catch sense if the distance between the players with conicting goals are less than a fixed constant l. In this sense, we obtain sufficient conditions for the completion of the pursuit and construct a strategy for the pursuer in each of the four different problems considered. Furthermore, we give examples to support our theoretical findings