Multiple positive solutions for singular periodic boundary value problems of impulsive differential equations in Banach spaces
type: Item
instance of: scholarly article
title: Multiple positive solutions for singular periodic boundary value problems of impulsive differential equations in Banach spaces
zbMATH Open document ID: 1237.34112
DOI: 10.1155/2011/493639
author: Hongxia Fan
author: Yongxiang Li
published in: Abstract and Applied Analysis
publication date: 2012-01-16T00:00:00Z
review text: The authors consider the following singular periodic boundary value problem with impulsive effects in a Banach space \[ \begin{aligned} & -u''(t)+M^2 u(t)=f(t, u(t)),\,\,\, t\in [0,2\pi], t\neq t_k,\\ &\Delta u|_{t=t_{k}}=I_{k}(u(t_{k})),\\ &\Delta u'|_{t=t_{k}}=-\bar I_{k}(u(t_{k})),\,\,\, k=1,2,\dots, m,\\ &u(0)=u(2\pi), \,\,\, u'(0)=u'(2\pi), \end{aligned} \] where \(M>0\) is constant, \(f(t,u)\) may be singular at \(t=0,\) and/or \(t=2\pi,\) \(f\in C[(0,2\pi)\times P, P],\) \(I_k, \bar I_k\in C[P,P],\) \(\Delta u|_{t=t_{k}}=u(t_{k}^+)-u(t_k^-),\) \(\Delta u'|_{t=t_{k}}=u'(t_{k}^+)-u'(t_k^-)\) and \(E\) is a Banach space partially ordered by a cone \(P\) of \(E.\) The existence of multiple positive solutions is proved by means of the fixed point index theory of strict set contraction operators. An example illustrating the main results is also presented.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5997801
zbMATH Keywords: impulsive differential equations
zbMATH Keywords: positive solutions
zbMATH Keywords: periodic boundary value problem
zbMATH Keywords: fixed point index theory
Wikidata QID: Q58654245
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/493639
OpenAlex ID: W1979496210
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description: scientific article; zbMATH DE number 5997801