In this paper, we investigated the minimax of the bifunction J : H 1 ( Ω ) x V 2 → R m x R n , such that J ( v 1 , v 2 ) = ( ( 1 2 a ( v 1 , v 1 ) − L ( v 1 ) ) , v 2 ) where a ( . , . ) is a finite symmetric bilinear bicontinuous, coercive form on H 1 ( Ω ) and L belongs to the dual of H 1 ( Ω ) .
In order to obtain the minimax point we use lagrangian functional.