Multiple positive solutions for first-order impulsive integrodifferential equations on the half line in Banach spaces
type: Item
instance of: scholarly article
title: Multiple positive solutions for first-order impulsive integrodifferential equations on the half line in Banach spaces
zbMATH Open document ID: 1247.34125
DOI: 10.1155/2011/634612
author: Dajun Guo
published in: International Journal of Differential Equations
publication date: 2012-03-08T00:00:00Z
review text: The author considers the existence of multiple positive solutions for first-order impulsive integrodifferential equations on the half line in a real Banach space \(E\): \[ \begin{aligned} & u' (t) = f (t,u(t), (Tu) (t), (Su) (t)), \\ &\Delta u |_{t=t_k} = i_k (u(t_k)), \quad k= 1,2.3. \dots, \\ &u (\infty) = \gamma u(\mu) + \beta u (0),\end{aligned} \] where \[ \begin{aligned} (Tu) (t) = \int^t_0 K (t,s ) u (s) ds,\\ (Su) (t) = \int^\infty_0 H (t,s) u (s) ds. \end{aligned} \] Fixed point theorems of cone expansion are used. A new cone is introduced. Two examples are given.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6013211
zbMATH Keywords: impulsive integrodifferential equations
zbMATH Keywords: real Banach space
zbMATH Keywords: cone
Wikidata QID: Q58686818
reviewed by: Miklavž Mastinšek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/634612
OpenAlex ID: W2005216659
cites work: Q3994493
cites work: Multiple positive solutions for first order nonlinear impulsive integro-differential equations in a Banach space
cites work: Q3814282
cites work: Q4716265
description: scientific article; zbMATH DE number 6013211