Concentration phenomena for fourth-order elliptic equations with critical exponent
Date
2004-10-14
Authors
Hammami, Mokhless
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We consider the nonlinear equation
Δ2u = u n+4/n-4 - εu
with u > 0 in Ω and u = Δu = 0 on ∂Ω. Where Ω is a smooth bounded domain in ℝn, n ≥ 9, and ε is a small positive parameter. We study the existence of solutions which concentrate around one or two points of Ω. We show that this problem has no solutions that concentrate around a point of Ω as ε approaches 0. In contract to this, we construct a domain for which there exists a family of solutions which blow-up and concentrate in two different points of Ω as ε approaches 0.
Description
Keywords
Fourth order elliptic equations, Critical Sobolev exponent, Blowup solution
Citation
Hammami, M. (2004). Concentration phenomena for fourth-order elliptic equations with critical exponent. <i>Electronic Journal of Differential Equations, 2004</i>(121), pp. 1-22.
Rights
Attribution 4.0 International