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 $$x_1, x_{2},..., x_{m}$$ x 1 , x 2 , . . . , x m 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 $$x_{i_1}(\tau _1)=y(\tau _1),..., x_{i_d} (\tau _d)=y(\tau _d)$$ x i 1 ( τ 1 ) = y ( τ 1 ) , . . . , x i d ( τ d ) = y ( τ d ) for some pairwise distinct numbers $$i_1, i_{2},..., i_d \in \left\{ 1, 2,..., m\right\}$$ i 1 , i 2 , . . . , i d ∈ 1 , 2 , . . . , m and times $$0