Quasilinear elliptic inequalities with Hardy potential and nonlocal terms

Abstract

We study the quasilinear elliptic inequality $$ -Δ_m u - \fracμ{|x|^m}u^{m-1} \geq (I_α*u^p)u^q \quad\mbox{ in }\mathbb{R}^N\setminus \overline B_1, N\geq 1, $$ where $p>0$, $q,\hat{I}¼\in \mathbb{R}$, $m>1$ and $I_{\hat{I}}\pm$ is the Riesz potential of order $\hat{I}\pm \in (0,N)$. We obtain necessary and sufficient conditions for the existence of positive solutions.

20 pages