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| We consider semilinear elliptic equations involving the polyharmonic operator $\Delta^{\!m}$, power nonlinearities, and positive radial weights. Specifically, we classify all unbounded radial solutions on open balls by their behavior near the boundary and study the asymptotics of solutions that diverge to infinity ("large solutions"). Extending a classical result for the case $m=1$, we obtain the first-order asymptotics (the "blow-up profile") of large radial solutions in the biharmonic case, $m=2$. For arbitrary $m$, we prove the weaker assertion that large radial solutions remain between positive multiples of the expected blow-up profile. |
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