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

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

2007-09-18

arxiv.org/abs/0709.2878v1

Mathematics

Analysis of PDEs

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

Scientific paper

Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^{4}$ such that for some integer $d\geq1$ its $d$-th singular cohomology group with coefficients in some field is not zero, then problem {\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega, u=\Delta u=0 & \hbox{on}\partial\Omega, has a solution blowing-up, as $\rho\to0$, at $m$ points of $\Omega$, for any given number $m$.

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