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

Publicly Available Published by De Gruyter March 10, 2016

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 H²_2,0(Ω) while sup_Ω u_∊ →∞, we describe the asymptotics of u_∊ as ∊ → 0.

Received: 2004-02-02

Published Online: 2016-03-10

Published in Print: 2004-11-01