Existence of T-solution for degenerated problem via Minty’s lemma

We study the existence result of solutions for the nonlinear degenerated elliptic problem of the form, —div( a ( x, u ,∇ u )) = F in Ω, where Ω is a bounded domain of ℝ N , N ≥ 2, a : Ω × ℝ × ℝ N → ℝ N is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but they verify only the large monotonicity. The second term F belongs to W −1, p ′ (Ω, w *). The existence result is proved by using the L 1 -version of Minty’s lemma.