Abstract
The main goal of this paper, by using the theorems of Lions, J.L. et al.[21, 22], is to study a distributed control problem for n x n coupled systems of elliptic type with an infinite number of variables. Yet the problem considered there is more general than the one in [1-8,10,11,13,20]. The necessary and sufficient conditions for optimality of the control are obtained and the set of inequalities that defining the optimal control of these systems are also obtained. Several mathematical examples for derived optimality conditions are presented