Mei-Hua Yang

Existence and uniqueness of solutions to Hardy-H\'enon boundary-value problems

We consider the elliptic equation $$ -\Delta u=d(x)^\alpha u^p,\quad x\in \Omega\quad (\text{or } x\in\mathbb{R}^N\setminus \overline{\Omega}), $$ where \(\alpha, p \in \mathbb{R}\), \(d(x) = \text{dist} (x,\partial\Omega)\) and \(\Omega\subset\mathbb{R}^N\) \((N\geq 3)\) is a bounded smooth domain. We establish estima...