Neumann problems for nonlinear elliptic equations with L¹ data

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In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is equation* cases -Δₚ u -div (c(x)|u|ᵖ⁻²u)) =f & inΩ, (|∇ u|ᵖ⁻²∇ u+ c(x)|u|ᵖ⁻²u)· n=0 & on∂ Ω, cases 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.