In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \begin{ equation*} \begin{ cases} -\Delta_{ p} u -\text{ div} (c(x)|u|^{ p-2}u)) =f & \text{ in}\ \Omega, \\ \left( |\nabla u|^{ p-2}\nabla u+ c(x)|u|^{ p-2}u \right)\cdot\underline n=0 & \text{ on}\ \partial \Omega \,, \end{ cases} \end{ equation*} when $f$ is just a summable function. Our approach allows also to deduce a stability result for renormalized solutions and an existence result for operator with a zero order term.
Categories: math.AP