| Abstract: |
| This talk concerns an elliptic boundary problem of a supercritical elliptic equation in the half space $\partial\mathbb{R}^N:=\{(x_1,\ldots,x_N)\in\mathbb{R}^N: x_N>0\}$ with an inhomogeneous Dirichlet boundary condition $u=\lambda\varphi$ on $\partial\mathbb{R}^N$. Here $\varphi$ is a nonnegative non-zero function on $\mathbb{R}^N$ with suitable conditions and $\lambda>0$ is a parameter. Under a Joseph--Lundgren subcritical condition, we give a complete classification of the existence/nonexistence of solutions. Briefly, our result states that there is a threshold constant $\lambda^*>0$ such that the problem has a solution if and only if $0< \lambda\le\lambda^*$. |
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