| Abstract: |
| This talk is devoted to the existence and nonexitence of stable solutions to a fractional Hardy-H\`{e}non equation $(-\Delta)^s u = |x|^l |u|^{p-1} u$ in $\mathbf{R}^N$. For this equation, we show the nonexistence of stable solutions when $p$ is subcritical in the sense of Joseph-Lundgren and the existence of a family of stable solutions when $p$ is critical or supercritical in the sense of Joseph-Lundgren. In addition, we reveal some properties of the family of stable solutions as well as the multiple existence of Joseph-Lundgren critical exponents for some range of $s$, $N$ and $l$. This is based on joint work with Shoichi Hasegawa (Waseda University) and Tatsuki Kawakami (Ryukoku University). |
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