Periodic boundary value problems for first order impulsive integro-differential equations of mixed type
type: Item
instance of: scholarly article
title: Periodic boundary value problems for first order impulsive integro-differential equations of mixed type
zbMATH Open document ID: 1057.45002
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-20T00:00:00Z
review text: The authors consider the periodic boundary value problem for first-order impulsive integro-differential equations of mixed type: \[ \begin{gathered} x'(t)= f(t,x(t),[Tx](t),[Sx](t)),\;t\in I,\;t\neq t_k\quad (k= 1,2,\dots, p),\\ \Delta x(t_k)= I_k(x(t_k)),\\ x(0)= x(2n),\end{gathered} \] where \[ \begin{gathered} f\in C(I\times R^1\times R^1\times R^1; R^1),\;I= [0,2n],\;I_k\in C(R^1; R^1),\\ \Delta x(t_k)= x(t^+_k)- x(t^-_k),\quad 0< t_1< t_2<\cdots< t_p< 2n,\\ [Sx])t_= \int^t_0 K(t,s)x(s)\,ds,\;[Tx](t)= \int^{2n}_0 H(t,s) x(s)\,ds.\end{gathered} \] Applying Lakshmikantham's monotone iterative technique and the method of upper and lower solutions they obtain extremal solutions of the above problem.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45M15
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 2093813
zbMATH Keywords: Impulsive integro-differential equation
zbMATH Keywords: Periodic boundary value problem
zbMATH Keywords: Upper and lower solution
zbMATH Keywords: Monotone iterative technique
zbMATH Keywords: periodic solution
zbMATH Keywords: extremal solutions
author: Zhimin He
author: Xiaoming He
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.12.047
OpenAlex ID: W2035491628
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DOI: 10.1016/J.JMAA.2003.12.047
description: scientific article; zbMATH DE number 2093813