Uniqueness of positive solutions for singular nonlinear boundary value problems
type: Item
instance of: scholarly article
title: Uniqueness of positive solutions for singular nonlinear boundary value problems
zbMATH Open document ID: 0873.34015
author: Fu-Hsiang Wong
author: Shiueh-Ling Yu
published in: Hiroshima Mathematical Journal
publication date: 1997-10-27T00:00:00Z
review text: The authors consider the uniqueness of positive solutions of the singular nonlinear differential equation \[ u''(r)+{\textstyle \frac mr} u'(r)+f(r,u(r))=0 \quad\text{in }(t_1,t_2), \qquad m\geq 0,\;0\leq t_1<t_2<\infty \] with one of the following sets of boundary conditions \[ u(t_1)= k_1\geq 0,\quad u(t_2)= k_2\geq 0, \qquad u'(t_1)= u(t_2)=0, \] \[ a_1u(t_1)+ b_1u'(t_1)=0, \qquad a_2u(t_2)+ b_2u'(t_2)=0, \] where \(a_i,b_i\in (-\infty,\infty)\) satisfy \(a_i^2+b_i^2\neq 0\), \(i=1,2\), \(u\in C^1[t_1,t_2]\), \(f:(t_1,t_2)\times (0,\infty)\to(- \infty,\infty)\) is local Lipschitz continuous in \(u\in(0,\infty)\) for each fixed \(r\in(t_1,t_2)\), \(f(r,u)/u\) is strictly decreasing with respect to \(u\in(0,\infty)\) for each fixed \(r\in(t_1,t_2)\). The purpose of the paper is to give an extension of known results.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 986951
zbMATH Keywords: nonlinear
zbMATH Keywords: uniqueness
zbMATH Keywords: positive solutions
zbMATH Keywords: singular nonlinear differential equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206127358
OpenAlex ID: W1532742688
DOI: 10.32917/HMJ/1206127358
description: scientific article; zbMATH DE number 986951