Liouville type theorems for a quasilinear elliptic differential inequality with weighted nonlocal source and gradient absorption terms

This work is concerned with the nonexistence of nontrivial nonnegative weak solutions for a strongly p-coercive elliptic differential inequality with weighted nonlocal source and gradient absorption terms in the whole space. Under the condition that the positive weight in the absorption term is either a sufficiently small constant or more general, we establish new Liouville type results containing the critical case. The key ingredient in the proof is the rescaled test function method developed by Mitidieri and Pohozaev.