“…In reproducing the argument used in Hamed to prove point (i) in Hamed,, proposition 3 (see also Hamed, proposition 9), ie, the “cone invariance property,” which is stated in Proposition (i) below, we introduce the following truncated nonlinearities: Here, χ is a smooth cutoff function outside the ball of radius ρ =2 in (L 2 (Ω)) 3 . Indeed, let with χ ( r )=1 for 0≤ r ≤1, χ ( r )=0 for r ≥2, and | χ ′ ( r )|≤2 for r ≥0 (which is null outside the ball of radius ).…”