We provide the classification of the positive solutions to $-\Delta_p u =u^{p^*-1}$ in $\mathcal {D}^{1,p}(\R^N)$ in the case $2<p<N$. Since the case $1<p\leq2$ is already known this provides the complete classification for $1<p<N$.
On positive solutions for $(p,q)$-Laplace equations with two parameters
On the regularity theory for mixed anisotropic and nonlocal $p$-Laplace equations and its applications to singular problems
The solution of the $\infty$-Laplace equation in the square
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