## Topological Methods in Nonlinear Analysis

### Fractional Hardy-Sobolev elliptic problems

#### Abstract

In this paper, we study the following singular nonlinear elliptic problem $$\begin{cases} \displaystyle (-\Delta)^{ \alpha/ 2} u=\lambda |u|^{r-2}u+\mu\frac{|u|^{q-2}u}{|x|^{s}} &\text{in }\Omega, \\ u=0 &\text{on } \partial\Omega, \end{cases} \tag{P}$$ 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 55, Number 1 (2020), 257-280.

Dates
First available in Project Euclid: 6 March 2020

https://projecteuclid.org/euclid.tmna/1583463629

Digital Object Identifier
doi:10.12775/TMNA.2019.075

Zentralblatt MATH identifier
07199343

#### Citation

Yang, Jianfu; Yu, Jian. Fractional Hardy-Sobolev elliptic problems. Topol. Methods Nonlinear Anal. 55 (2020), no. 1, 257--280. doi:10.12775/TMNA.2019.075. https://projecteuclid.org/euclid.tmna/1583463629

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