# Singular limits for the bi-laplacian operator with exponential nonlinearity in $R^4$ - Mathematics > Analysis of PDEs

Singular limits for the bi-laplacian operator with exponential nonlinearity in $R^4$ - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^{4}$ such that forsome integer $d\geq1$ its $d$-th singular cohomology group with coefficients insome field is not zero, then problem{\Delta^{2}u- ho^{4}kxe^{u}=0 and \hbox{in}\Omega,u=\Delta u=0 and \hbox{on}\partial\Omega,has a solution blowing-up, as $ho\to0$, at $m$ points of $\Omega$, for anygiven number $m$.

Author: Mónica Clapp, Claudio Muñoz, Monica Musso

Source: https://arxiv.org/