Boundary-value problems for systems of first-order partial differential inclusions (Q1975882)

The boundary value problems for the systems related to the first-order partial differential inclusion system \[ \begin{cases} x'(t)= f(t,x(t), y(t), p(t))\\ y'(t)= g(t,x(t),y(t),p(t))\\ p(t)\in P(t,x(t), y(t))\end{cases} \] are considered. Existence, uniqueness and continuity of the Frankowska solution to the corresponding system are given in terms of the concept ``graphical envelope'' of a suitable set-valued mapping.