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

Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami

研究成果: Article査読

10 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2059-2078
ページ数20
ジャーナルCalculus of Variations and Partial Differential Equations
54
2
DOI
出版ステータスPublished - 2015 10月 22

ASJC Scopus subject areas

  • 分析
  • 応用数学

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