Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition

Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We consider the semilinear elliptic equation – Δu = up, p > 1, u = u (x,t) x ∈ ℝN+, t > 0, with a dynamical boundary condition. We show that, for p < (N+1)/(N-1), there exist no nontrivial nonnegative local-in-time solutions. Furthermore, in the case P > (N+1)/(N-1)$$p>(N+1)/(N-1), we determine the optimal slow decay rate at spatial infinity for initial data giving rise to global bounded positive solutions.

Original languageEnglish
Pages (from-to)2059-2078
Number of pages20
JournalCalculus of Variations and Partial Differential Equations
Volume54
Issue number2
DOIs
Publication statusPublished - 2015 Oct 22

Keywords

  • 35B40
  • 35J25
  • 35J91

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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