Existence results for impulsive second-order periodic problems
type: Item
instance of: scholarly article
title: Existence results for impulsive second-order periodic problems
zbMATH Open document ID: 1084.34031
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-11-22T00:00:00Z
review text: The authors prove existence results for the nonlinear impulsive periodic boundary value problem \[ u''=f(t,u,u');\; u(t_i^+)=J_i(u(t_i)), \; u'(t_i^+)=M_i(u'(t_i)), \; i=1,2, \ldots,m; \] \[ u(0)=u(T), \; u'(0)=u'(T). \] Here, \(f\) is a Carathéodory function and \(J_i\) and \(M_i \) are continuous functions. They prove that if \(| f| \) is bounded in \(L^1\) and there exists a pair of nonordered lower and upper solutions, then this problem has at least one solution that satisfies additional properties with respect to the lower and the upper solutions.
reviewed by: Alberto Cabada
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 2117566
zbMATH Keywords: second-order nonlinear ordinary differential equation with impulses
zbMATH Keywords: periodic solutions
zbMATH Keywords: lower and upper functions
zbMATH Keywords: Leray-Schauder topological degree
zbMATH Keywords: a priori estimates
author: Irena Rachůnková
author: Milan Tvrdý
MaRDI profile type: Publication
full work available at URL: j.na.2004.07.006
OpenAlex ID: W2144221170
cites work: Q4325523
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DOI: 10.1016/J.NA.2004.07.006
description: scientific article; zbMATH DE number 2117566