We prove comparison principles, uniqueness, regularity and symmetry results for p-regular distributional solutions of quasilinear very weak elliptic equations of coercive type and to related inequalities. The simplest model examples are -Δ_pu+|u|^(q-1)u=h on R^N, where q>p-1>0 and -div(
abla u/sqrt(1+|
abla u|^2)+|u|^(q-1)u=h on RN, with q>0 and h∈L^1_loc(R^N).
