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We study the quasilinear elliptic inequality $$ -\Delta_m u -\frac{\mu}{|x|^m}u^{m-1} \geq (I_\alpha*u^p)u^q \quad\mbox{ in}\mathbb{R}^N\setminus \overline B_1, N\geq 1, $$ where $p>0$, $q, \mu \in\mathbb{R}$, $m>1$ and $I_\alpha$ is the Riesz potential of order $\alpha\in(0,N)$. We obtain necessary and sufficient conditions for the existence ofpositive solutions.

Quasilinear elliptic inequalities with Hardy potential and nonlocal terms