Existence results for second order boundary value problem of impulsive dynamic equations on time scales
type: Item
instance of: scholarly article
title: Existence results for second order boundary value problem of impulsive dynamic equations on time scales
zbMATH Open document ID: 1060.34017
author: Mouffak Benchohra
author: Sotiris K. Ntouyas
author: Abdelghani Ouahab
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-20T00:00:00Z
review text: The authors establish existence results for an impulsive second-order dynamic equation on time scales \(-y^{\Delta\Delta}(t)=f(t,y(t))\), \(t\in[0,1]\subseteq{\mathbb T}\), \(t\neq t_k\), \(k=1,\dots,m\), where \({\mathbb T}\) is a time scale (nonempty closed subset of \({\mathbb R}\)) and where the solution \(y(t)\) satisfies \(y(0)=0=y(1)\), and \(y(t_k^+)-y(t_k^-)\) and \(y^\Delta(t_k^+)-y^\Delta(t_k^-)\) are functions of \(y(t_k^-)\) and \(y^\Delta(t_k^-)\), respectively. The solution \(y(t)\) does not need to be continuous at \(t=t_k\). The technique used is that of the fixed-point theory. Hypothesis (H1) of the paper contains the \textit{continuity} of the forward jump function \(\sigma:{\mathbb T}\to{\mathbb T}\) (which excludes time scales with left-dense/right-scattered points). It seems that this condition is not needed.
reviewed by: Roman Šimon Hilscher
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 2093817
zbMATH Keywords: time scale
zbMATH Keywords: boundary value problem
zbMATH Keywords: fixed-point theorem
zbMATH Keywords: impulsive dynamic equation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.02.057
OpenAlex ID: W1999783726
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DOI: 10.1016/J.JMAA.2004.02.057
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description: scientific article; zbMATH DE number 2093817