On a maximum principle for weak solutions of some quasi-linear elliptic equations

We address some generalizations of the maximum principle for weak solutions of quasi-linear equations of the type − Δ p u + b | u | p − 2 u = f ( ⋅ , u ) in an open set Ω ⊂ R N . The novelty of our work concerns more general assumptions both on the right-hand side f and the set Ω .