Neumann problems for nonlinear elliptic equations with lower order terms

In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is { λ|u|p−2u − ∆pu − div(c(x)|u|p−2u) + b(x)|∇u|p−2∇u = f in Ω, (|∇u|p−2∇u + c(x)|u|p−2u) · n = 0 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, λ > 0, the datum f belongs to the dual space of W 1,p(Ω) or to Lebesgue space L1(Ω). Finally the coefficients b, c belong to appropriate Lebesgue spaces or Lorentz spaces. Existence results for weak solutions or renormalized solutions are proved under small- ness assumptions on the coefficients b and c.