Singular limits for the bi-laplacian operator with exponential nonlinearity in R4\R^4

preprint2007arXivOpen access

Abstract

Let ΩΩ be a bounded smooth domain in R4\mathbb{R}^{4} such that for some integer d≥1d\geq1 its dd-th singular cohomology group with coefficients in some field is not zero, then problem {Δ^{2}u-ρ^{4}k(x)e^{u}=0 & \hbox{in}Ω, u=Δu=0 & \hbox{on}\partialΩ, has a solution blowing-up, as ρ→0ρ\to0, at mm points of ΩΩ, for any given number mm.

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