Two point boundary value problems for the equation \(({\Psi{}}(T,X'))'=F(T,X,X')\)
type: Item
instance of: scholarly article
title: Two point boundary value problems for the equation \(({\Psi{}}(T,X'))'=F(T,X,X')\)
zbMATH Open document ID: 0755.34019
DOI: 10.1016/0022-247X(92)90323-6
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The author proves some existence theorems for the boundary value problem \(x'=\varphi(t,y)\), \(y'=g(t,x,y)\), \(x\in E\), where \(g:[0,1]\times\mathbb{R}^ 2\to\mathbb{R}\) and \(\varphi(t,y)y\geq 0\), \(g\) satisfies a Bernstein-Nagumo type condition, and \(E\) is a closed linear subspace of \(C^ 1([0,1];\mathbb{R})\) of codimension two, such that for each \(u\in E\) there exists \(r_ 0=r_ 0(u)\in[0,1]\) such that \(| u(t)|\leq| u(t_ 0)|\) and \(u'(t_ 0)=0\). The results are then applied to boundary value problems for the equation \((\psi(t,x'))'=f(t,x,x')\), \(x\in E\).
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 62792
zbMATH Keywords: boundary value problem
zbMATH Keywords: Bernstein-Nagumo type condition
author: Antonio Tineo
reviewed by: Abdelkader Boucherif
MaRDI profile type: Publication
cites work: Solvability of some nonlinear boundary value problems
cites work: Existence of solutions for some nonlinear singular boundary value problems
cites work: Nonlinear boundary value problems for some classes of ordinary differential equations
cites work: Q4724080
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cites work: The Sturm-Liouville problem for the equation \(X''=P(T,X)Q(X')\)
description: scientific article; zbMATH DE number 62792