Remarks on comparison principles for p-Laplacian with extension to (p, q)-Laplacian

Our purpose is to generalize some recent comparison principles for operators driven by p-Laplacian to a wide class of quasilinear equations including (p,q)-Laplacian. It turns out, in particular, that adding a q-Laplacian to p-Laplacian allows to weaken the assumptions needed on the Hamiltonian of lower order terms. The results are specialized in the case that the Hamiltonian has at most polynomial growth in the gradient with coefficients depending on x and u.