Stable solutions of $−\Delta u = f(u)$ in $\mathbb{R}^N$

Louis Dupaigne; Alberto Farina

doi:10.4171/jems/217

JournalsjemsVol. 12, No. 4pp. 855–882

Stable solutions of $- Δ u = f (u)$ in $R^{N}$

Louis Dupaigne
Université Picardie Jules Verne, Amiens, France
Alberto Farina
Université de Picardie Jules Verne, Amiens, France

$Stable solutions of $−\Delta u = f(u)$ in $\mathbb{R}^N$ cover$

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Abstract

Several Liouville-type theorems are presented for stable solutions of the equation $- ∆ u = f (u)$ in $R^{N}$ , where $f > 0$ is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.

Cite this article

Louis Dupaigne, Alberto Farina, Stable solutions of $- Δ u = f (u)$ in $R^{N}$ . J. Eur. Math. Soc. 12 (2010), no. 4, pp. 855–882

DOI 10.4171/JEMS/217