Anti-periodic boundary value problems for nonlinear higher order impulsive differential equations
type: Item
instance of: scholarly article
title: Anti-periodic boundary value problems for nonlinear higher order impulsive differential equations
zbMATH Open document ID: 1152.34021
author: Yuji Liu
author: Zhanji Gui
published in: Taiwanese Journal of Mathematics
publication date: 2008-07-29T00:00:00Z
review text: The authors consider the impulsive boundary value problem for higher order differential equation \[ \begin{aligned} &x^{(n)}(t) = f(t,x(t),x'(t),\ldots,x^{(n-1)}(t)),\quad t \in [0,1]\setminus\{t_1,\ldots,t_p\}, \\ &\triangle x^{(i)}(t_k) = I_{i,k}(x(t_k),x'(t_k),\ldots,x^{(n-1)}(t_k)), \quad k = 1,\ldots,p,\;i = 0,\ldots,n-1,\\ &x^{(i)}(0) = -x^{(i)}(T),\quad i = 0,\ldots,n-1, \end{aligned} \] where \(0 < t_1 < \ldots < t_p < 1\), \(f\) is an impulsive Carathéodory function, \(I_{i,k}\) are continuous functions. Sufficient conditions for the existence of at least one solution of the problem are obtained. The proofs of the main results are based on the Fredholm operator theory.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5304995
zbMATH Keywords: anti-periodic boundary value problem
zbMATH Keywords: higher order impulsive differential equation
zbMATH Keywords: fixed point theorem
zbMATH Keywords: growth condition
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500574163
OpenAlex ID: W4251265820
DOI: 10.11650/TWJM/1500574163
description: scientific article; zbMATH DE number 5304995