Calculus of Variations and Geometric Measure Theory
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F. Gazzola - H. C. Grunau

Radial entire solutions for supercritical biharmonic equations

created by gazzola on 30 May 2005
modified on 14 Dec 2005


Accepted Paper

Inserted: 30 may 2005
Last Updated: 14 dec 2005

Journal: Math. Annal.
Year: 2005


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 $n\ge13$.


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