Points de Nash Dans le Cas de Fonctionnelles Quadratiques et Jeux Differentiels lineaires a N Personnes

In this article, we consider the problem of Nash points for quadratic functionals in Hilbert spaces. Necessary and sufficient conditions of optimality are given. We apply the results to N-person differential games. Open-loop and closed-loop solutions are considered. When there are no constraints, two types of Riccati equations are obtained. We completely develop the parabolic case, generalizing results of A. Friedman [2] who considered finite-dimensional systems. The infinite-dimensional systems that are modeled are the ones which represent distributed parameter systems as in Lions [4].