Critical Exponent Elliptic Equations on the Half-Space: Uniqueness and Explicit Solutions

Azam Nouri

We prove that all positive solutions of $-\hat{I}”u=u^{\frac{2n}{n-2}}$ on the upper half space ${\mathbb{R}}_{+}^n$ (for $n\ge 3$) satisfying the boundary condition $D_{x_n}u = -u^{\f…