Multiple capture in a differential game with mixed constraints on controls of players

We study a simple motion multiple capture pursuit differential game of m pursuers x1,x2,..,xm and one evader y. On the first k coordinates of the control function of each player a geometric constraint is imposed, and the other coordinates are subjected to an integral constraint. If xi1(τ1)=y(τ1),..,xid(τd)=y(τd) for some pairwise distinct numbers i1,i2,..,id∈1,2,..,m and times 0<τ1≤τ2≤..≤τd, then we say that d-multiple capture occurs. We obtain a sufficient condition for multiple capture to occur and construct strategies for the pursuers.