Existence results for second-order impulsive boundary value problems on time scales
type: Item
instance of: scholarly article
title: Existence results for second-order impulsive boundary value problems on time scales
zbMATH Open document ID: 1166.34308
author: Jianli Li
author: Jianhua Shen
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-03-09T00:00:00Z
review text: The authors consider the impulsive boundary value problem on time scales \[ \begin{aligned} &-y^{\Delta\Delta}(t)=f(t,y(t)) \,\, \text{a.e}\,\, t\in J:[0,1]\setminus\{t_1,\dots,t_p\},\\ &y(t_k^+)-y(t_k^-)=I_k(y(t_k^-)), \,\,\, k=1,\dots, p,\\ &y^{\Delta}(t_k^+)-y^{\Delta}(t_k^-)=\tilde I_k(y(t_k^-)), \quad k=1,\dots, p,\\ &y(0)=y(1)=0. \end{aligned} \] Some new results are obtained for the existence of one or three positive solutions, by using a fixed point theorem due to Krasnoselskii and Zabreiko, and the Leggett-Williams fixed point theorem, respectively.
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5526373
zbMATH Keywords: boundary value problem
zbMATH Keywords: impulses
zbMATH Keywords: fixed point theorem
zbMATH Keywords: time scales
reviewed by: Sotiris K. Ntouyas
MaRDI profile type: Publication
full work available at URL: j.na.2008.02.047
OpenAlex ID: W2047554750
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DOI: 10.1016/J.NA.2008.02.047
description: scientific article; zbMATH DE number 5526373