Existence theorems for three-point boundary value problem
type: Item
instance of: scholarly article
zbMATH Open document ID: 0994.34009
author: Haishen Lü
author: Chengkui Zhong
publication date: 2002-10-13T00:00:00Z
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1659052
zbMATH Keywords: singular three-point boundary value problems
zbMATH Keywords: nonlinear value problems
zbMATH Keywords: nonlinear alternative
MaRDI profile type: Publication
title: Existence theorems for three-point boundary value problem
published in: Annals of Differential Equations
review text: Basing on a nonlinear alternative, sufficient conditions for the existence of solutions are obtained for the singular boundary value problem NEWLINE\[NEWLINE(\varphi(y'))'= q(x) f(x,y,y'),\quad 0< x< 1,\quad y(0)= A,\quad y(\eta)- y(1)= (\eta- 1)B.NEWLINE\]NEWLINE Here, \(\varphi\) is strictly increasing, \(q\) is positive on \((0,1)\) and integrable. The functions \(\varphi\), \(q\), \(f\) are continuous. The numbers \(\eta\in (0,1)\), \(A\), \(B\) are given. The solution \(y\) is continuously differentiable on \([0,1]\) with \((\varphi(y'))'\) continuous on \((0,1)\).
reviewed by: Sergei A. Brykalov
description: scientific article; zbMATH DE number 1659052