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

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

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    15 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

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    Keywords

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

    ASJC Scopus subject areas

    • Analysis

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