Neumann problems for nonlinear elliptic equations with L^1 data

Abstract In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is { − Δ p u − div ( c ( x ) | u | p − 2 u ) ) = f in Ω , ( | ∇ u | p − 2 ∇ u + c ( x ) | u | p − 2 u ) ⋅ n ̲ = 0 on ∂ 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.