Neumann problems for nonlinear elliptic equations with L1L1 data

In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is{−Δpu−div(c(x)|u|p−2u))=finΩ,(|∇u|p−2∇u+c(x)|u|p−2u)⋅n̲=0on∂Ω, when f is just a summable function. Our approach also allows us to prove a stability result for renormalized solutions and an existence result for operator with a zero order term.