Minimax Solution of Functional Hamilton-Jacobi Equations for Neutral Type Systems

We consider the Cauchy problem for a functional Hamilton-Jacobi equation with coinvariant derivatives corresponding to dynamical systems of the neutral type. A definition of minimax (generalized) solution of this problem is given and its existence, uniqueness, and also continuous dependence on the parameters are proved. The dependence of the minimax solution on information images is established, which, in particular, permits showing the consistency of the introduced definition with the definition of minimax solution for Hamilton-Jacobi partial differential equations.