“…Since many infinite dimensional equilibrium problems have ordering cone empty, these usual conditions cannot be used to guarantee the strong duality. This is the case of all optimization problems or variational inequalities connected with network equilibrium problems, the obstacle problems, the elastic plastic torsion problems (see [1,[5][6][7][8][9][11][12][13][14]16,19,20,23]) which use positive cones of L p (Ω) or Sobolev spaces. Recently, in [9,8,10,18] the authors overcome this important difficulty by introducing a condition called Assumption S which ensures the strong duality.…”