In this paper we construct single and multiple blowing-up solutions to the mean field equation $-\Delta u=λ V(x)e^u/\int_\Omega V(x) e^u$ in Ω, $u=0$ on $\partial \Omega$, where Ω is a smooth bounded domain in R^2, V is a smooth function positive somewhere in Ω and λ is a positive parameter.
Esposito, P., Grossi, M., Pistoia, A. (2005). On the existence of blowing-up solutions for a mean field equation. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 22(2), 227-257 [10.1016/j.anihpc.2004.12.001].
On the existence of blowing-up solutions for a mean field equation
ESPOSITO, PIERPAOLO;
2005-01-01
Abstract
In this paper we construct single and multiple blowing-up solutions to the mean field equation $-\Delta u=λ V(x)e^u/\int_\Omega V(x) e^u$ in Ω, $u=0$ on $\partial \Omega$, where Ω is a smooth bounded domain in R^2, V is a smooth function positive somewhere in Ω and λ is a positive parameter.File in questo prodotto:
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