Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one

János Engländer, Péter L. Simon

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2 Citations (Scopus)

Abstract

In this article, we consider a semilinear elliptic equations of the form Δu + f(u) = 0, where / is a concave function. We prove for arbitrary dimensions that there is no solution bounded in (0, 1). The significance of this result in probability theory is also discussed.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalElectronic Journal of Differential Equations
Volume2006
Publication statusPublished - Jan 24 2006

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Keywords

  • Branching brownian-motion
  • Kpp-equation
  • Positive bounded solutions
  • Semilinear elliptic equations

ASJC Scopus subject areas

  • Analysis

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