Initial value problems for the second order mixed monotone type of impulsive differential equations in Banach spaces
type: Item
instance of: scholarly article
title: Initial value problems for the second order mixed monotone type of impulsive differential equations in Banach spaces
zbMATH Open document ID: 0964.34008
author: Jinli Sun
author: Yihai Ma
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-07-22T00:00:00Z
review text: The authors consider initial value problems to the impulsive differential equation of the form \[ u''- f(x, u,u')=\theta,\quad x\in J,\quad x\neq x_i,\quad \Delta u|_{x=x_i}= I(u(x_i)),\quad \Delta u'|_{x= x_i}=\widetilde I(u(x_i)), \] \[ i= 1,2,\dots, m\quad u(0)= w_0,\quad u'(0)= w_1, \] where \(f\) is a continuous function of its arguments, \(J= [0,1]\), \(I_i\) and \(\widetilde I_i\) are impulsive sources (continuous functions) propagating the impulsive effect, \(0< x_1< x_2<\cdots< x_m< 1\), are given fixed points. The authors use the coupled fixed-point theorem for mixed monotone condensing operators to obtain an interesting existence and uniqueness theorem.
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34L30
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 1497259
zbMATH Keywords: impulsive differential equations
zbMATH Keywords: fixed-point theorem
reviewed by: Drumi Bainov
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6858
OpenAlex ID: W2050369145
cites work: Q3995625
cites work: Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming
cites work: Q3994493
cites work: Coupled fixed points of nonlinear operators with applications
DOI: 10.1006/JMAA.2000.6858
description: scientific article; zbMATH DE number 1497259