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On the influence of the kernel of the bi-harmonic operator on fourth order equations with exponential growth

Pages: 875 - 882, Issue Special, September 2007

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Frédéric Robert - Université de Nice-Shopia Antipolis, Laboratorie J.-A. Dieudonné, Parc Valrose, 06108 Nice Cedex 2, France (email)

Abstract: Continuing the analysis of [1, 9, 10], we discuss in this note the influence of the Kernel of the bi-harmonic operator $\Delta^2$ on the behavior of families of solutions to $\Delta^2u = e^(4u)$ on a four-dimensional domain of the Euclidean space. We also make a remark on the Paneitz-type equation in the context of compact Riemannian manifolds.

Keywords:  Paneitz equation, Exponential growth.
Mathematics Subject Classification:  Primary 35J35; Secondary 35B40.

Received: September 2006;      Revised: March 2007;      Published: September 2007.