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dc.contributor.authorHammami, Mokhless ( )
dc.identifier.citationHammami, M. (2004). Concentration phenomena for fourth-order elliptic equations with critical exponent. Electronic Journal of Differential Equations, 2004(121), pp. 1-22.en_US

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.

dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectFourth order elliptic equationsen_US
dc.subjectCritical Sobolev exponenten_US
dc.subjectBlowup solutionen_US
dc.titleConcentration phenomena for fourth-order elliptic equations with critical exponenten_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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