F. Gladiali

The H\'enon equation beyond the critical Sobolev exponent

We consider the Dirichlet problem $-\Delta u=|x|^\alpha u^p$, $u>0$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega\subset R^N$, $N\ge 3$, is a bounded domain containing the origin and $\alpha>0$. We prove that a solution exists for every exponent $1<p<p_\alpha=\frac{N+2+2\alpha}{N-2}$, in particular in the whole...