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We give a qualitative analysis of sequences of stationary solutions to the supercritical problem   \[ -\Delta u= |u|^{p-1} u \quad \hbox{in}\ \Omega,\quad p&gt;\frac{n+2}{n-2}. \]    A consequence of the analysis is the existence of positive singular weak solutions on a convex domain when   $p \in \big (\frac {n+2}{n-2}, \frac {n+1}{n-3}\big)$  , with only isolated singularities.

Analysis of Blow-up Locus and Existence of Weak Solutions for Nonlinear Supercritical Problems