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

Abstract

Let $\Omega$ be a bounded smooth domain in ${\mathbb{R}}^4$ such that for some integer $d\ge 1$ 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 & \hbox{in}Ω, u=Δu=0 & \hbox{on}\partialΩ, has a solution blowing-up, as $\rho \to 0$, at $m$ points of $\Omega$, for any given number $m$.

30 pages, to appear in Ann. IHP Non Linear Analysis

References in corpus (1)

• Singular limits for 4-dimensional semilinear elliptic problems with exponential nonlinearity