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 −Δpu+b|u|p−2u=f(⋅,u)−Δpu+b|u|p−2u=f(⋅,u) in an open set Ω⊂RNΩ⊂RN. The novelty of our work concerns more general assumptions both on the right-hand side ff and the set ΩΩ.