Some general existence principles for ordinary differential equations
type: Item
instance of: scholarly article
title: Some general existence principles for ordinary differential equations
zbMATH Open document ID: 0798.34003
DOI: 10.12775/TMNA.1993.029
author: Marlène Frigon
author: Donal O'Regan
published in: Topological Methods in Nonlinear Analysis
publication date: 1994-11-01T00:00:00Z
review text: The authors establish some general existence principles for the first order initial value problem \(y'=f(t,y)\), \(0<t<T\), \(y(0)=a\) and the second order boundary value problem \((py')'=f(t,y,py')\), \(0<t<1\), \(-\alpha y(0) + \beta \lim_{t \to 0 + } p(t)y'(t) = c\) \(\alpha \geq 0\), \(\beta\geq 0\), \(ay(1) + b \lim_{t \to 1-} p(t)y'(t) = d\) \(a\geq 0\), \(b \geq 0\) and \(\alpha + a>0\). The results of the paper extend and complement the existing theory in the literature. In particular, \(f\) need not be continuous or even Carathéodory.
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 591504
zbMATH Keywords: existence
zbMATH Keywords: first order initial value problem
zbMATH Keywords: second order boundary value problem
reviewed by: Anthony D. Osborne
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 591504