Liouville properties for differential inequalities with (p, q)-Laplacian operator

In this paper, we establish several Liouville-type theorems for a class of nonhomogenenous quasilinear inequalities. In the first part, we prove various Liouville results associated with nonnegative solutions when the reaction is a pure power of the solution, while in the second part we consider gradient type nonlinearities. To the best of our knowledge, the technique used in the latter case is completely new and provides an alternative approach to the capacity method of Mitidieri-Pohozaev provided higher regularity is available.