On maximum and comparison principles for parabolic problems with the p-Laplacian

We investigate strong and weak versions of maximum and comparison principles for a class of quasilinear parabolic equations with the p-Laplacian ∂tu−Δpu=λ|u|p−2u+f(x,t) under zero boundary and nonnegative initial conditions on a bounded cylindrical domain Ω×(0,T), λ∈R, and f∈L∞(Ω×(0,T)). Several related counterexamples are given