Positive solutions for a singular second-order ordinary differential equation
type: Item
instance of: scholarly article
title: Positive solutions for a singular second-order ordinary differential equation
zbMATH Open document ID: 1124.34317
author: N. E. Zubov
published in: Lobachevskii Journal of Mathematics
publication date: 2007-04-11T00:00:00Z
full work available at URL: https://eudml.org/doc/233201
full work available at URL: 122.html
review text: The authors consider the positive solutions for the singular second-order ordinary differential equation \[ \frac{\varphi''}{\sqrt{1+| \varphi'| ^2}}-\lambda\frac{| \varphi'| ^2}{\varphi(1+| \varphi'| ^2)^m}+f(t)=0,\quad 0<t<1, \] with one of the following boundary conditions \[ \varphi(1)=\varphi(0)=0, \] \[ \varphi(1)=\varphi(0)=\varphi'(1)=\varphi'(0)=0, \] where \(\lambda>0, m\geq\frac{1}{2}, f(t)\in C^1[0,1]\) and \(f(t)>0\) on \([0,1]\). By the classical method of elliptic regularization, the existence results are established.
reviewed by: Dingyong Bai
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5141824
zbMATH Keywords: singular differential equation
zbMATH Keywords: positive solution
zbMATH Keywords: existence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5141824