Journal of the European Mathematical Society


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Volume 12, Issue 4, 2010, pp. 855–882
DOI: 10.4171/JEMS/217

Published online: 2010-06-02

Stable solutions of −∆u = f(u) in ℝN

Louis Dupaigne[1] and Alberto Farina[2]

(1) Université Picardie Jules Verne, Amiens, France
(2) Université de Picardie Jules Verne, Amiens, France

Several Liouville-type theorems are presented for stable solutions of the equation −∆u = f(u) in ℝN, 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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Dupaigne Louis, Farina Alberto: Stable solutions of −∆u = f(u) in ℝN. J. Eur. Math. Soc. 12 (2010), 855-882. doi: 10.4171/JEMS/217