American Institute of Mathematical Sciences

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2007, 2007(Special): 875-882. doi: 10.3934/proc.2007.2007.875

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

Frédéric Robert 1,

1. 

Université de Nice-Shopia Antipolis, Laboratorie J.-A. Dieudonné, Parc Valrose, 06108 Nice Cedex 2, France

Received  September 2006 Revised  March 2007 Published  September 2007

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 35B4.
Citation: Frédéric Robert. On the influence of the kernel of the bi-harmonic operator on fourth order equations with exponential growth. Conference Publications, 2007, 2007 (Special) : 875-882. doi: 10.3934/proc.2007.2007.875
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