Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions
type: Item
instance of: scholarly article
title: Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions
zbMATH Open document ID: 1069.39002
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: The authors investigate a lot of conditions under which the first-order impulsive difference equation with periodic boundary condition \[ \begin{gathered} \Delta x(n)= f(n,x(n)),\quad n\neq n_k,\quad n_k\in \{0,1,\dots, N\}:= J,\\ \Delta x(n_k)= I_k(x(n_k)),\quad k= 1,2,\dots, p,\\ x(0)= x(N),\end{gathered} \] where \(f\in C(J\times\mathbb{R},\mathbb{R})\), \(I_k\in C(\mathbb{R},\mathbb{R})\), \(0< n_1< n_2<\cdots< n_p< N\), and \(N\) is a positive integer. Among others the method of upper and lower solution is used to prove the existence and uniqueness of so-called extremal solutions to the problem under consideration.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2117994
zbMATH Keywords: Impulsive difference equation
zbMATH Keywords: Periodic boundary condition
zbMATH Keywords: Upper and lower solution
zbMATH Keywords: Monotone iterative technique
zbMATH Keywords: Extremal solutions
author: Zhimin He
author: Xian-Ming Zhang
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
full work available at URL: j.amc.2003.08.013
OpenAlex ID: W2038269211
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DOI: 10.1016/J.AMC.2003.08.013
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description: scientific article; zbMATH DE number 2117994