Green's function and positive solutions for a second-order singular boundary value problem with integral boundary conditions and a delayed argument
type: Item
instance of: scholarly article
title: Green's function and positive solutions for a second-order singular boundary value problem with integral boundary conditions and a delayed argument
zbMATH Open document ID: 1470.34171
DOI: 10.1155/2014/393187
author: Xuemei Zhang
author: Meiqiang Feng
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper investigates the expression and properties of Green's function for a second-order singular boundary value problem with integral boundary conditions and delayed argument \(- x^{\prime \prime} \left(t\right) - a \left(t\right) x' \left(t\right) + b \left(t\right) x \left(t\right) = \omega \left(t\right) f \left(t, x \left(\alpha \left(t\right)\right)\right), t \in \left(0, 1\right); x' \left(0\right) = 0, x \left(1\right) - \int_0^1 h \left(t\right) x \left(t\right) d t = 0\), where \(a \in \left(\left[0, 1\right], \left[0, + \infty\right)\right), b \in C \left(\left[0, 1\right], \left(0, + \infty\right)\right)\) and, \(\omega\) may be singular at \(t = 0\) or/and at \(t = 1\). Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel'skii's fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 7022300
Wikidata QID: Q59037243
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/393187
OpenAlex ID: W2099236863
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description: scientific article; zbMATH DE number 7022300