Upper and lower solutions method for a class of singular fractional boundary value problems with \(p\)-Laplacian operator
type: Item
instance of: scholarly article
title: Upper and lower solutions method for a class of singular fractional boundary value problems with \(p\)-Laplacian operator
zbMATH Open document ID: 1209.34005
DOI: 10.1155/2010/971824
author: Hongjun Xiang
author: J. H. Wang
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/227986
review text: The authors establish the existence of at least one positive solution for a class of singular Riemann-Liouville fractional order boundary value problems with \(p\)-Laplacian operator satisfying four point boundary conditions. Using the upper and lower solutions method, properties of Green's function, and, applying Schauder's fixed point theorem, the existence of at least one positive solution of the four point fractional order boundary value problem is established. Here, the singularity of the nonlinear function of the boundary value problem is taken for three different cases. The established results are verified by an example at the end. Reviewer's remark: The concept of upper and lower solutions is not used properly. The remaining part of the paper is good.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5791642
zbMATH Keywords: fractional boundary value problem
zbMATH Keywords: p-Laplacian equation
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: positive solution
Wikidata QID: Q58649197
reviewed by: K. Rajendra Prasad
MaRDI profile type: Publication
OpenAlex ID: W1997778563
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description: scientific article; zbMATH DE number 5791642