Data evento: 
Wednesday, May 29, 2019 - 10:00
Begoña Barrios Barrera
 Universidad de La Laguna
Titolo: The sharp exponent in the study of the nonlocal H\'enon equation in $\mathbb{R}^{N}$. 
Abstract: We will consider the nonlocal H\'enon equation 
$$(-\Delta)^s u= |x|^{\alpha} u^{p},\quad \mathbb{R}^{N},$$
where $(-\Delta)^s$ is the fractional Laplacian operator with $0<s<1$, $-2s<\alpha$, $p>1$ and $N>2s$. We prove a Liouville result for positive solutions in the optimal range of the nonlinearity, that is, when
$$1<p<p^*_{\alpha, s}:=\frac{N+2\alpha+2s}{N-2s}.$$
Moreover, we prove that a kind of bubble solution, that is, a fast decay positive radially symmetric solutions, exists when $p=p_{\alpha, s}^{*}$.

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