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Asymptotic Profile for a Fourth Order PDE with Critical Exponential Growth in Dimension Four

Frédéric Robert and Michael Struwe

Abstract

Let Ω be a smooth domain of R4. In this paper, we consider a family (u)∊>0 of positive solutions in C4(Ω̅) to the equation

where λ ∈ ℝ. Assuming that u→ 0 weakly in H22,0(Ω) while supΩ u →∞, we describe the asymptotics of u as ∊ → 0.

Received: 2004-2-2
Published Online: 2016-3-10
Published in Print: 2004-11-1

© 2016 by Advanced Nonlinear Studies, Inc.