New result for a class of impulsive differential equation with integral boundary conditions
type: Item
instance of: scholarly article
title: New result for a class of impulsive differential equation with integral boundary conditions
zbMATH Open document ID: 1263.34033
author: Wei Ding
author: Yu Wang
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2013-01-25T00:00:00Z
review text: The authors consider the impulsive boundary value problem \[ \begin{aligned} y''(t)& = f(t,y(t)), \quad 0 < t < 1,\quad t \neq t_k,\\ \triangle y|_{t=t_k} &= I_k(y(t_k)), \quad k = 1,\dotsc, n,\\ \triangle y'|_{t=t_k} &= \bar I_k(y(t_k),y'(t_k)), \quad k = 1,\dotsc,n,\\ y(0) - ay'(0) &= \int_0^1 g_0(s)y(s)\, \text{d}s,\\ y(1) - by'(1) &= \int_0^1 g_1(s)y(s)\, \text{d}s, \end{aligned} \] where \(0 < t_1 < \dotsb < t_n < 1\), \(f\), \(I_k\), \(\bar I_k\), \(g_0\), \(g_1\) are continuous, \(a,b \geq 0\). Using Krasnosel'skii's fixed point theorem, sufficient conditions ensuring the existence of positive solutions are obtained.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 6130737
zbMATH Keywords: boundary value problem
zbMATH Keywords: integral boundary conditions
zbMATH Keywords: positive solution
zbMATH Keywords: second-order ODE
zbMATH Keywords: impulses at fixed times
Wikidata QID: Q115358673
MaRDI profile type: Publication
full work available at URL: j.cnsns.2012.09.021
OpenAlex ID: W2006116451
DOI: 10.1016/J.CNSNS.2012.09.021
description: scientific article; zbMATH DE number 6130737