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

Louis Dupaigne, Alberto Farina

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Source: Crossref

Published: Jun 2, 2010

DOI: 10.4171/jems/217

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Source 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.

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