Fixed points of increasing operators and solutions of nonlinear impulsive integro-differential equations in Banach space
type: Item
instance of: scholarly article
title: Fixed points of increasing operators and solutions of nonlinear impulsive integro-differential equations in Banach space
zbMATH Open document ID: 0962.45006
DOI: 10.1016/S0362-546X(99)00117-0
author: Jiang Zhu
author: Shiqi Zhang
author: Xianling Fan
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-01-17T00:00:00Z
review text: The authors study the initial value problem (IVP) of the nonlinear impulsive integro-differential equations in Banach space. \[ x'= f(t,x,Tx,Sx),\;t\neq t_i;\quad \Delta x|_{t=t_i} =I_i(x),\;i=1,2,\dots,p; \quad x(0)=x_0. \] They prove some new fixed-point theorems for increasing operators, which are also the generalization of known results. Then, they use these fixed point theorems to discuss the existence of the extremal solutions of IVP, without assuming that \(f,k,h\), and \(I_i(i=1,2,\dots,p)\) are continuous.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1513362
zbMATH Keywords: initial value problem
zbMATH Keywords: nonlinear impulsive integro-differential equations
zbMATH Keywords: Banach space
zbMATH Keywords: fixed-point theorems
zbMATH Keywords: increasing operators
zbMATH Keywords: extremal solutions
reviewed by: V. Lakshmikantham
MaRDI profile type: Publication
Wikidata QID: Q127634222
full work available at URL: s0362-546x(99)00117-0
OpenAlex ID: W2073896906
description: scientific article; zbMATH DE number 1513362