Stable solutions of −∆<em>u</em> = <em>f</em>(<em>u</em>) in ℝ<sup><em>N</em></sup>

  • Louis Dupaigne

    Université Picardie Jules Verne, Amiens, France
  • Alberto Farina

    Université de Picardie Jules Verne, Amiens, France


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 −∆<em>u</em> = <em>f</em>(<em>u</em>) in ℝ<sup><em>N</em></sup>. J. Eur. Math. Soc. 12 (2010), no. 4, pp. 855–882

DOI 10.4171/JEMS/217