TY - JOUR

T1 - Uniqueness of sign-changing radial solutions for Δu-u+|u|p-1u = 0 in some ball and annulus

AU - Tanaka, Satoshi

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number 26400182 .
Publisher Copyright:
© 2016 Elsevier Inc.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

KW - Modified Bessel functions

KW - Scalar field equation

KW - Sign-changing radial solutions

KW - Uniqueness

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U2 - 10.1016/j.jmaa.2016.02.036

DO - 10.1016/j.jmaa.2016.02.036

M3 - Article

AN - SCOPUS:84960475390

VL - 439

SP - 154

EP - 170

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -