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




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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/







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