@article{4ff2676a1fe9499aa24dbf1da4818e61,

title = "On the uniqueness of solutions of a semilinear equation in an annulus",

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).",

keywords = "Annulus, Energy function, Semilinear equation, Subcritical, Uniqueness",

author = "Carmen Cort{\'a}zar and Marta Garc{\'i}a-Huidobro and Pilar Herreros and Satoshi Tanaka",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary: 35J61, 35A02; Secondary: 35A24. Key words and phrases. Uniqueness, annulus, semilinear equation, subcritical, energy function. This research was supported by FONDECYT-1190102 for the first and second author, and FONDECYT-1170665 for the third author and by JSPS KAKENHI Grant Number 19K03595 and 17H01095 for the fourth author. ∗ Corresponding author. Publisher Copyright: {\textcopyright} 2021 American Institute of Mathematical Sciences. All rights reserved.",

year = "2021",

month = apr,

day = "1",

doi = "10.3934/cpaa.2021029",

language = "English",

volume = "20",

pages = "1479--1496",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "4",

}