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Quasilinear elliptic inequalities with Hardy potential and nonlocal terms
Published online by Cambridge University Press: 24 July 2020
Abstract
We study the quasilinear elliptic inequality
\[ -\Delta_m u - \frac{\mu}{|x|^m}u^{m-1} \geq (I_\alpha*u^p)u^q \quad\mbox{in }\mathbb{R}^N\setminus \overline B_1, N\geq 1, \]
$p>0$,
$q, \mu \in \mathbb {R}$,
$m>1$ and
$I_\alpha$ is the Riesz potential of order
$\alpha \in (0,N)$. We obtain necessary and sufficient conditions for the existence of positive solutions.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 3 , June 2021 , pp. 1075 - 1093
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press
References
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