Minimal positive solutions to some singular second-order differential equations
type: Item
instance of: scholarly article
title: Minimal positive solutions to some singular second-order differential equations
zbMATH Open document ID: 1002.34015
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-01-01T00:00:00Z
review text: The author studies the boundary value problem \[ x''+ f(t, x,x')= 0,\quad 0< t< 1,\quad x(0)= x'(1)= 0, \] where the function \(f\) is continuous and satisfies the inequality \(f(t,x,y)\leq k(t) p(x) q(y)\) with functions \(k\), \(p\) and \(q\) satisfying certain conditions. A solution \(x(t)\) to this problem is said to be minimal positive if it belongs to \(C[0,1]\cap C^2(0,1)\), \(x(t)> 0\) for \(t\in (0,1]\) and no other positive solution is smaller than it. The author finds which condition the functions \(k\), \(p\) and \(q\) must satisfy to guarantee the existence of a minimal positive solution.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 1744289
zbMATH Keywords: minimal positive solutions
zbMATH Keywords: singular second-order differential equations
author: Guang Chong Yang
reviewed by: Ludvík Janoš
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7748
OpenAlex ID: W2052574895
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DOI: 10.1006/JMAA.2001.7748
description: scientific article; zbMATH DE number 1744289