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2020 Fractional Hardy-Sobolev elliptic problems
Jianfu Yang, Jian Yu
Topol. Methods Nonlinear Anal. 55(1): 257-280 (2020). DOI: 10.12775/TMNA.2019.075

Abstract

In this paper, we study the following singular nonlinear elliptic problem \begin{equation} \begin{cases} \displaystyle (-\Delta)^{ \alpha/ 2} u=\lambda |u|^{r-2}u+\mu\frac{|u|^{q-2}u}{|x|^{s}} &\text{in }\Omega, \\ u=0 &\text{on } \partial\Omega, \end{cases} \tag{P} \end{equation} where $\Omega$ is a smooth bounded domain in $\mathbb R^N(N\geq 2)$ with $0\in \Omega$, $\lambda,\mu> 0$, $0< s\leq\alpha$, $(-\Delta)^{\alpha/ 2}$ is the spectral fractional Laplacian operator with $0< \alpha< 2$. We establish existence results and nonexistence results of problem (P) for subcritical, Sobolev critical and Hardy-Sobolev critical cases.

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Jianfu Yang. Jian Yu. "Fractional Hardy-Sobolev elliptic problems." Topol. Methods Nonlinear Anal. 55 (1) 257 - 280, 2020. https://doi.org/10.12775/TMNA.2019.075

Information

Published: 2020
First available in Project Euclid: 6 March 2020

zbMATH: 07199343
MathSciNet: MR4100386
Digital Object Identifier: 10.12775/TMNA.2019.075

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.55 • No. 1 • 2020
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