Mathematische Annalen

, Volume 334, Issue 4, pp 905–936

Radial entire solutions for supercritical biharmonic equations

Article

DOI: 10.1007/s00208-005-0748-x

Cite this article as:
Gazzola, F. & Grunau, HC. Math. Ann. (2006) 334: 905. doi:10.1007/s00208-005-0748-x

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.

Mathematics Subject Classification (2000)

35J6035J30

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Fakultät für MathematikOtto-von-Guericke-UniversitätMagdeburgGermany