Positive and negative solutions of a quasi–linear elliptic equation by a Mountain Pass method and truncature techniques Original Research Article

The existence of a positive and a negative solution of a problem of the type -Δu+f(x,u,∇u)=0-Δu+f(x,u,∇u)=0 in ΩΩ, u=0u=0 on ∂Ω∂Ω is proved, when f has a growth at infinity depending both on u and on ∇u∇u. The techniques are based on an iterative scheme of Mountain Pass “approximated” solutions and the use of a suitable truncature method.