On the uniqueness of solutions of a semilinear equation in an annulus

Carmen Cortázar, Marta García-Huidobro, Pilar Herreros, Satoshi Tanaka

Research output: Contribution to journalArticlepeer-review

Abstract

We establish the uniqueness of positive radial solutions of (equation presented) where A := Aa;b = fx 2 Rn : A < jxj < bg, 0 < a < b ≤ 1. We assume that the nonlinearity f ∈ C[0;1) ∩ C1(0;1) is such that f(0) = 0 and satisfies some convexity and growth conditions, and either f(s) > 0 for all s > 0, or has one zero at B > 0, is non positive and not identically 0 in (0;B) and it is positive in (B;1).

Original languageEnglish
Pages (from-to)1479-1496
Number of pages18
JournalCommunications on Pure and Applied Analysis
Volume20
Issue number4
DOIs
Publication statusPublished - 2021 Apr 1

Keywords

  • Annulus
  • Energy function
  • Semilinear equation
  • Subcritical
  • Uniqueness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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