The existence of positive solutions of nonlinear singular second-order boundary value problems
type: Item
instance of: scholarly article
title: The existence of positive solutions of nonlinear singular second-order boundary value problems
zbMATH Open document ID: 1007.34021
DOI: 10.1016/S0895-7177(01)00089-9
published in: Mathematical and Computer Modelling
publication date: 2002-06-13T00:00:00Z
review text: New results guaranteeing the existence of positive solutions to the boundary value problem \[ (1/p(t))(p(t) x'(t))'+ q(t) f(t,x(t),p(t) x'(t))= 0,\quad 0< t< 1,\quad \lim_{t\to 0+} p(t) x'(t)= 0= x(1), \] are given. Here, \(q\in C(0,1)\) and \(p\in C[0,1]\cap C^1(0, 1)\) are positive on \((0,1)\) and such that \[ \int^1_0 {dt\over p(t)}< \infty,\quad \int^1_0 p(t)q(t) dt< \infty, \] and \(f: [0,1]\times (0,\infty)\times (-\infty, 0]\to \mathbb{R}^0\) is continuous. The function \(f\) may be singular at \(x= 0\) and \(t=0\) or/and \(t=1\). To prove the existence theorems, the authors construct upper and lower solutions to the problem considered and use properties of the egress points and the consequent mapping. However, they apply the standard Schauder fixed-point theorem.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1755304
zbMATH Keywords: singularity
zbMATH Keywords: positive solutions
zbMATH Keywords: boundary value problem
zbMATH Keywords: egress points
zbMATH Keywords: consequent mapping
author: Sotiris K. Ntouyas
author: Panos K. Palamides
reviewed by: Petio S. Kelevedjiev
MaRDI profile type: Publication
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full work available at URL: s0895-7177(01)00089-9
OpenAlex ID: W1970826405
description: scientific article; zbMATH DE number 1755304