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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 :...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Hindawi Publishing Corporation
2013
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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. |
format | Online Article Text |
id | pubmed-3856140 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2013 |
publisher | Hindawi Publishing Corporation |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT zhaodaliang multiplepositivesolutionsfornonlinearfractionalboundaryvalueproblems AT liuyansheng multiplepositivesolutionsfornonlinearfractionalboundaryvalueproblems |