Uniqueness of sign-changing radial solutions for Δu-u+|u|p-1u = 0 in some ball and annulus

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4 Citations (Scopus)

Abstract

The following Dirichlet problem is considered, where Ω is either an annulus or a ball in RN and p > 1. The uniqueness of radial solutions having exactly k-1 nodes is shown for the following cases: Ω is a sufficiently thin annulus; Ω is a certain small ball, N ≥ 4 and 1 < p < N/(N-2); Ω is the unit ball, N =3 and 1 < p ≤ 3; Ω is any annulus or any ball, but p >1 is sufficiently close to 1 and N = 3, 5 or 7.

Original languageEnglish
Pages (from-to)154-170
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume439
Issue number1
DOIs
Publication statusPublished - 2016 Jul 1

Keywords

  • Modified Bessel functions
  • Scalar field equation
  • Sign-changing radial solutions
  • Uniqueness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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