Increase of power leads to a bilateral solution to a strongly nonlinear elliptic coupled system.

In this paper, we analyze the following nonlinear elliptic problem A (u) = ρ (u) | ∇ φ | 2 in Ω , div (ρ (u) ∇ φ) = 0 in Ω , u = 0 on ∂ Ω , φ = φ 0 on ∂ Ω. where A(u) = −div a(x, u, ∇u) is a Leray-Lions operator of order p. The second member of the first equation is only in L¹(Ω). We prove the existence of a bilateral solution by an approximation procedure, the keypoint being a penalization technique. [ABSTRACT FROM AUTHOR]