Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem

The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. Th...

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Main Authors: Wen Lian, Zhanbing Bai
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/8196918
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author Wen Lian
Zhanbing Bai
author_facet Wen Lian
Zhanbing Bai
author_sort Wen Lian
collection DOAJ
description The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. The conclusion relies on the fixed-point index theory and the Leray-Schauder degree theory. The growth conditions of the nonlinearity with respect to the first eigenvalue of the related linear operator is given to guarantee the existence and multiplicity.
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institution Kabale University
issn 2314-8896
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language English
publishDate 2020-01-01
publisher Wiley
record_format Article
series Journal of Function Spaces
spelling doaj-art-5fe957bdeb9a4c9bbb54d67a4df57eb62025-02-03T06:06:31ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/81969188196918Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value ProblemWen Lian0Zhanbing Bai1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThe existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. The conclusion relies on the fixed-point index theory and the Leray-Schauder degree theory. The growth conditions of the nonlinearity with respect to the first eigenvalue of the related linear operator is given to guarantee the existence and multiplicity.http://dx.doi.org/10.1155/2020/8196918
spellingShingle Wen Lian
Zhanbing Bai
Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
Journal of Function Spaces
title Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
title_full Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
title_fullStr Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
title_full_unstemmed Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
title_short Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
title_sort eigenvalue criteria for existence of positive solutions to fractional boundary value problem
url http://dx.doi.org/10.1155/2020/8196918
work_keys_str_mv AT wenlian eigenvaluecriteriaforexistenceofpositivesolutionstofractionalboundaryvalueproblem
AT zhanbingbai eigenvaluecriteriaforexistenceofpositivesolutionstofractionalboundaryvalueproblem