A sharper condition for the solvability of a three-point second order boundary value problem
type: Item
instance of: scholarly article
title: A sharper condition for the solvability of a three-point second order boundary value problem
zbMATH Open document ID: 0874.34014
author: Chaitan P. Gupta
author: Sergei Trofimchuk
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-11-13T00:00:00Z
review text: Let \(f:[0,1] \times\mathbb{R}^2 \to\mathbb{R}\) be a function satisfying Carathéodory's conditions and \(e(t)\in L^1[0,1]\). Let \(\eta\in(0,1)\), \(\alpha\in\mathbb{R}\), \(\alpha>1\), \(\alpha\eta \neq 1\) be given. This paper is concerned with the problem of existence of a solution for the three-point boundary value problem \[ x''(t)=f \bigl(t,x(t), x'(t)\bigr)+ e(t),\;0<t<1,\;x(0)=0,\;x(1)= \alpha x(\eta). \tag{*} \] In the general case this problem was studied by the first author as a multipoint boundary value problem. In the present paper, sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case.
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 1005679
zbMATH Keywords: Carathéodory's conditions
zbMATH Keywords: three-point boundary value problem
reviewed by: Pavel Talpalaru
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5252
OpenAlex ID: W2029514159
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DOI: 10.1006/JMAA.1997.5252
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description: scientific article; zbMATH DE number 1005679