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arXiv · 2009.04319

Quasilinear elliptic inequalities with Hardy potential and nonlocal terms

Marius Ghergu·Paschalis Karageorgis·Gurpreet Singh
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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 $p>0$, $q, μ\in \mathbb{R}$, $m>1$ and $I_α$ is the Riesz potential of order $α\in (0,N)$. We obtain necessary and sufficient conditions for the existence of positive solutions.

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Marius Ghergu, Paschalis Karageorgis, Gurpreet Singh. 2020-09-09. Quasilinear elliptic inequalities with Hardy potential and nonlocal terms. https://doi.org/10.1017/prm.2020.50

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