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Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems

This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem [Formula: see text] u(t) = f(t, u(t), u′(t)), 0 < t < 1, u(1) = u′(1) = u′′(0) = 0, where 2 < α ≤ 3 is a real number, [Formula: see text] is the Caputo fractional derivative, and f :...

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Detalles Bibliográficos
Autores principales: Zhao, Daliang, Liu, Yansheng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3856140/
https://www.ncbi.nlm.nih.gov/pubmed/24348162
http://dx.doi.org/10.1155/2013/473828
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author Zhao, Daliang
Liu, Yansheng
author_facet Zhao, Daliang
Liu, Yansheng
author_sort Zhao, Daliang
collection PubMed
description This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem [Formula: see text] u(t) = f(t, u(t), u′(t)), 0 < t < 1, u(1) = u′(1) = u′′(0) = 0, where 2 < α ≤ 3 is a real number, [Formula: see text] is the Caputo fractional derivative, and f : [0,1]×[0, +∞) × R → [0, +∞) is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii's fixed point theorem and Leggett-Williams fixed point theorem, some new existence criteria for fractional boundary value problem are established; secondly, by applying a new extension of Krasnoselskii's fixed point theorem, a sufficient condition is obtained for the existence of multiple positive solutions to the considered boundary value problem from its auxiliary problem. Finally, as applications, some illustrative examples are presented to support the main results.
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spelling pubmed-38561402013-12-16 Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems Zhao, Daliang Liu, Yansheng ScientificWorldJournal Research Article This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem [Formula: see text] u(t) = f(t, u(t), u′(t)), 0 < t < 1, u(1) = u′(1) = u′′(0) = 0, where 2 < α ≤ 3 is a real number, [Formula: see text] is the Caputo fractional derivative, and f : [0,1]×[0, +∞) × R → [0, +∞) is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii's fixed point theorem and Leggett-Williams fixed point theorem, some new existence criteria for fractional boundary value problem are established; secondly, by applying a new extension of Krasnoselskii's fixed point theorem, a sufficient condition is obtained for the existence of multiple positive solutions to the considered boundary value problem from its auxiliary problem. Finally, as applications, some illustrative examples are presented to support the main results. Hindawi Publishing Corporation 2013-11-06 /pmc/articles/PMC3856140/ /pubmed/24348162 http://dx.doi.org/10.1155/2013/473828 Text en Copyright © 2013 D. Zhao and Y. Liu. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Zhao, Daliang
Liu, Yansheng
Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
title Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
title_full Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
title_fullStr Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
title_full_unstemmed Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
title_short Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
title_sort multiple positive solutions for nonlinear fractional boundary value problems
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3856140/
https://www.ncbi.nlm.nih.gov/pubmed/24348162
http://dx.doi.org/10.1155/2013/473828
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