We study Liouville theorems for problems of the form
divL (A (x, u, ∇L u)) + V(x)|u|p−2 u = a(x)|u|q−1 u
on RN
in the framework of Carnot groups. Here A is a vector-valued function satisfying Carathéodory condition
and ∇L denotes an horizontal gradient, V is a given singular potential, a is a measurable scalar function and
q > p − 1. Particular emphasis is given to the case when V is a Hardy or Gagliardo–Nirenberg potential. The
results are new even in the canonical Euclidean setting.
