Minimax differential game with delay

The paper considers a minimax positional differential game with aftereffect based on the $i$-smooth analysis methodology. In the finite-dimensional (ODE) case for a minimax differential game, resolving mixed strategies can be constructed using the dynamic programming method. The report shows that the $i$-smooth analysis methodology allows one to construct counterstrategies in a completely similar way to the finite-dimensional case. Moreover as it is typical for the use of $i$-smooth analysis, in the absence of an aftereffect, all the results of the article pass to the corresponding results of the finite-dimensional theory of positional differential games.