Uniqueness of radially symmetric positive solutions for - Δ u + u = up in an annulus

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

In this article we prove that the semi-linear elliptic partial differential equation- Δ u + u = up in Ω,u > 0 in Ω, u = 0 on ∂ Ω possesses a unique positive radially symmetric solution. Here p > 1 and Ω is the annulus {x ∈ RN | a < | x | < b}, with N ≥ 2, 0 < a < b ≤ ∞. We also show the positive solution is non-degenerate.

Original languageEnglish
Pages (from-to)1198-1209
Number of pages12
JournalJournal of Differential Equations
Volume245
Issue number5
DOIs
Publication statusPublished - 2008 Sep 1

Keywords

  • Non-degeneracy
  • Non-linear elliptic equation
  • Radially symmetric solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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