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Radial entire solutions for supercritical biharmonic equations

by Filippo Gazzola, Hans-Christoph Grunau.

Series: 2005-14, Preprints

35J40 Boundary value problems for higher-order elliptic equations

We prove existence and uniqueness (up to rescaling) of positive radial entire solutions of supercritical semilinear
biharmonic equations. The proof is performed with a shooting method which uses the
value of the second derivative at the origin as a parameter. This method also enables us to find finite time blow
up solutions. Finally, we study the convergence at infinity of regular solutions towards the
explicitly known singular solution.
It turns out that the convergence is different in space dimensions $n\le12$ and $n\ge13$.


This paper was published in:
Math. Annal. 334 , 905 - 936 (2006).