Concentration phenomena for fourth-order elliptic equations with critical exponent
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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.
CitationHammami, M. (2004). Concentration phenomena for fourth-order elliptic equations with critical exponent. Electronic Journal of Differential Equations, 2004(121), pp. 1-22.
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