Periodic boundary value problem for first order differential equations with impulses at variable times
type: Item
instance of: scholarly article
title: Periodic boundary value problem for first order differential equations with impulses at variable times
zbMATH Open document ID: 0876.34020
author: Ignacio Bajo
author: Eduardo Liz
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-04-29T00:00:00Z
review text: The authors study the periodic boundary value problem with impulses at variable times given by the system of equations \[ \begin{aligned} u'(t) &= f(t,u(t)), \qquad t\in J,\quad t\neq\gamma(u(t)),\\ u(t^+)&= u(t)+ I(u(t)), \quad t=\gamma(u(t)) \;\text{ and } u(0)= u(T),\end{aligned} \] where \(J=[0,T]\), \(f\in C(J\times \mathbb{R},\mathbb{R})\), \(I\in C'(\mathbb{R},\mathbb{R}^-)\) and \(\gamma\in C'(\mathbb{R},\mathbb{R})\). As the main result they show that the method of upper and lower solutions is applicable to this system.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A37
zbMATH DE Number: 1005485
zbMATH Keywords: periodic boundary value problem
zbMATH Keywords: impulses
zbMATH Keywords: upper and lower solutions
reviewed by: Ludvík Janoš
MaRDI profile type: Publication
OpenAlex ID: W2147270944
DOI: 10.1006/JMAA.1996.0424
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description: scientific article; zbMATH DE number 1005485