Esposito, Pierpaolo; Grossi, Massimo; Pistoia, Angela On the existence of blowing-up solutions for a mean field equation. (English) Zbl 1129.35376 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 22, No. 2, 227-257 (2005). In this paper we construct single and multiple blowing-up solutions to the mean field equation:\[ \begin{cases} - \Delta u = \lambda {{V(x)e^u } \over {\int_\Omega V(x)e^u } }& \text{in }\Omega, \\ u=0 & \text{on } \partial \Omega,\end{cases} \]where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^2\), \(V\) is a smooth function positive somewhere in \(\Omega\) and \(\lambda\) is a positive parameter. Cited in 135 Documents MSC: 35J60 Nonlinear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs 47N20 Applications of operator theory to differential and integral equations Keywords:mean field equation; peak solutions; Green’s function PDFBibTeX XMLCite \textit{P. Esposito} et al., Ann. Inst. Henri Poincaré, Anal. 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