05-14
Radial entire solutions for supercritical biharmonic equations
by Filippo Gazzola; Hans-Christoph Grunau
Preprint series: 05-14, Preprints
The paper is published: Math. Annal. 334 , 905 - 936 (2006).
- MSC:
- 35J40 Boundary value problems for higher-order, elliptic equations
Abstract: 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 $n\ge13$.
Notes: Copyright: Springer-Verlag.
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