First order impulsive initial and periodic problems with variable moments
type: Item
instance of: scholarly article
title: First order impulsive initial and periodic problems with variable moments
zbMATH Open document ID: 0930.34016
author: Donal O'Regan
author: Marlène Frigon
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-06-03T00:00:00Z
review text: The periodic impulsive problem \[ y'(t)= f(t,y(t)),\quad\text{a.e. }t\in [0,T], \] \[ y(t^+)= I_i(y(t)),\quad t= \tau_i(y(t)),\quad i= 1,\dots,k,\quad y(0)= y(T),\tag{1} \] is considered. Here, -- \(f:[0,T]\times \mathbb{R}^n\to \mathbb{R}^n\) is continuous and -- \(0<\tau_1(x)<\cdots< \tau_k(x)< \tau_{k+1}(x)\equiv T\), \(x\in\mathbb{R}^n\), are of class \(C^1\). Using a generalization of the Lefschetz fixed point theorem for a class of multivalued maps, sufficient conditions for the existence of a solution to (1) are found. The result is very important and can be generalized in many directions.
reviewed by: S. Kostadinov
Mathematics Subject Classification ID: 34B37
zbMATH DE Number: 1295275
zbMATH Keywords: impulsive differential equations
zbMATH Keywords: variable moments
zbMATH Keywords: periodic impulsive problem
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6336
OpenAlex ID: W2084236401
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DOI: 10.1006/JMAA.1999.6336
description: scientific article; zbMATH DE number 1295275