Existence and nonexistence of sign-changing solutions for singular semilinear equations on exterior domains
type: Item
instance of: scholarly article
title: Existence and nonexistence of sign-changing solutions for singular semilinear equations on exterior domains
zbMATH Open document ID: 1495.34051
author: Joseph A. Iaia
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2022-02-11T00:00:00Z
review text: In this paper, the author proves existence and nonexistence of radial solutions \(u\in C^1[R,\infty)\cap C^0[R,\infty)\) of the problem \[ \Delta u+K(r)f(u)=0\text{ in }\mathbb{R}^{N}\backslash B_{r},\, u=0\text{ on }\partial B_{R},\, u\to 0\text{ as }|x|\to\infty \] on \([R,\infty)\) using some of the following assumptions (i) \(f(u)=-(1/(|u|^{q-1}u))+g(u)\), \(f:\mathbb{R}\backslash 0\to\mathbb{R}\) is locally Lipschits, \(0<q<1\), \(g(0)=0\), \(f\) is odd, \(f<0\) on \((0,\beta)\), \(f>0\) on \((\beta,\infty)\), (ii) \(f(u)=|u|^{p-1}u+g_1(u)\), where \(\lim_{u\to\infty}((|g_1(u)|)/(|u|^{p}))=0\), \(p>1\), (iii) \(F(u)=\int_0^{u}f(s)ds(<0\) bounded below on \((0,\gamma),)/(>0\) on \((\gamma,\infty),)\) (iv) \(0<K(r)<C_1/r^\alpha\), \(\alpha>N+q(N-2)\), \(K(r)\) is continuously differentiable on \([R,\infty)\), \((v) 2(N-1)+((rK')/K)\geq 0\), where \(N>2\), \(B_{R}\) is the ball of radius \(R>0\) centered at the origin in \(\mathbb{R}^{N}\).
reviewed by: Ekin Ugurlu
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 7472465
zbMATH Keywords: sign-changing
zbMATH Keywords: multiple solutions
zbMATH Keywords: sublinear
zbMATH Keywords: exterior domains
MaRDI profile type: Publication
full work available at URL: j.na.2021.112752
OpenAlex ID: W4200405889
cites work: Positive solutions for a class of superlinear semipositone systems on exterior domains
cites work: Q5144876
cites work: Nonlinear scalar field equations. I: Existence of a ground state
cites work: Q3672366
cites work: Q4146134
cites work: Existence of solutions for semilinear problems with prescribed number of zeros on exterior domains
cites work: Q5118090
cites work: Positive solutions for infinite semipositone problems on exterior domains.
cites work: Positive radial solutions to classes of singular problems on the exterior domain of a ball
cites work: Semipositone problems with falling zeros on exterior domains
DOI: 10.1016/J.NA.2021.112752
description: scientific article; zbMATH DE number 7472465