The positive properties of Green's function for fractional differential equations and its applications
type: Item
instance of: scholarly article
title: The positive properties of Green's function for fractional differential equations and its applications
zbMATH Open document ID: 1274.34062
DOI: 10.1155/2013/531038
author: Fuquan Jiang
author: Xiaojie Xu
author: Zhongwei Cao
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: We consider the properties of Green's function for the nonlinear fractional differential equation boundary value problem: \(\mathbf{D}^\alpha_{0+}u(t) + f(t, u(t)) + e(t) = 0, 0 < t < 1, u(0) = u'(0) = \cdots = u^{(n-2)}(0) = 0, u(1) = \beta u(\eta)\), where \(n - 1 < \alpha \leq n, n \geq 3, 0 < \beta \leq 1, 0 \leq \eta \leq 1, \mathbf{D}^\alpha_{0+}\) is the standard Riemann-Liouville derivative. Here our nonlinearity \(f\) may be singular at \(u = 0\). As applications of Green's function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 6161347
Wikidata QID: Q58917040
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/531038
OpenAlex ID: W1988657832
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description: scientific article; zbMATH DE number 6161347