Singular limits for the bi-Laplacian operator with exponential nonlinearity in $\mathbb R^{4}$

Monica Musso; Mónica Clapp; Claudio Muñoz

doi:10.1016/j.anihpc.2007.09.002

JournalsaihpcVol. 25, No. 5pp. 1015–1041

Singular limits for the bi-Laplacian operator with exponential nonlinearity in $R^{4}$

Monica Musso
Departamento de Matemática, Pontificia Universidad Católica de Chile, Avenida Vicuna Mackenna 4860, Macul, Santiago, Chile; Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Mónica Clapp
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México DF, Mexico
Claudio Muñoz
Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile

$Singular limits for the bi-Laplacian operator with exponential nonlinearity in $\mathbb R^{4}$ cover$

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Abstract

Let $Ω$ be a bounded smooth domain in $R^{4}$ such that for some integer $d ⩾ 1$ its $d$ -th singular cohomology group with coefficients in some field is not zero, then problem

{Δ^{2} u - ρ^{4} k (x) e^{u} = 0 u = Δ u = 0 in Ω, on \partial Ω,

has a solution blowing-up, as $ρ \to 0$ , at $m$ points of $Ω$ , for any given number $m$ .

Cite this article

Monica Musso, Mónica Clapp, Claudio Muñoz, Singular limits for the bi-Laplacian operator with exponential nonlinearity in $R^{4}$ . Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 5, pp. 1015–1041

DOI 10.1016/J.ANIHPC.2007.09.002