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We study details of the boundary behavior of large radial solutions of semilinear elliptic equations involving the polyharmonic operator $\Delta^{\!m}$, power nonlinearities, and positive radial weights. Extending a known result for the case $m=1$, we obtain the first and second terms in the asymptotic expansions of all such solutions in the biharmonic case, $m=2$. For general $m$, we establish analogous expansions under additional conditions. We also describe situations in which these conditions fail and somewhat unexpected boundary behavior ensues. |
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