Radial entire solutions for supercritical biharmonic equations |
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Authors: | Filippo Gazzola Hans-Christoph Grunau |
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Institution: | 1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, Italy 2. Fakult?t für Mathematik, Otto-von-Guericke-Universit?t, Postfach 4120, 39016, Magdeburg, Germany
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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 smooth solutions towards the explicitly known singular solution. It turns out that the convergence is different in space
dimensions n ≤ 12 and n ≥ 13.
Financial support by the Vigoni programme of CRUI (Rome) and DAAD (Bonn) is gratefully acknowledged. |
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Keywords: | 35J60 35J30 |
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