UNIQUENESS FOR NEUMANN PROBLEMS FOR NONLINEAR ELLIPTIC EQUATIONS

In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is −(1 div((1+ |∇ +u|2 |∇)(p u− |22) )(/p2−∇2)u/2+ ∇c u(x )) −|u div(|p−2 cu (x )· |un _|p=−02u) = f in Ω, on ∂Ω, where Ω is a bounded domain of RN, N ≥ 2, with Lipschitz boundary, 1 < p < N , n is the outer unit normal to ∂Ω, the datum f belongs to L(p∗)(Ω) or to L1(Ω) and satisfies the compatibility condition Ω f dx = 0. Finally the coefficient c(x) belongs to an appropriate Lebesgue space