Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation D0+αu(t)+λa(t)f(t,u(t))=0,  0<t<1,   u(0)=0,  u(1)=Σi=1∞αiu(ξi) are considered, where 1<α≤2 is a real number, λ is a positive parameter, D0+α is the standard...

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Main Authors: Xiaoling Han, Hongliang Gao
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2011/725494
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spelling doaj-c4162dc9796e4dbdbcf5b8637cd3c76e2020-11-24T20:48:55ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472011-01-01201110.1155/2011/725494725494Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential EquationXiaoling Han0Hongliang Gao1Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaBy using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation D0+αu(t)+λa(t)f(t,u(t))=0,  0<t<1,   u(0)=0,  u(1)=Σi=1∞αiu(ξi) are considered, where 1<α≤2 is a real number, λ is a positive parameter, D0+α is the standard Riemann-Liouville differentiation, and ξi∈(0,1), αi∈[0,∞) with Σi=1∞αiξiα-1<1, a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,∞),[0,∞)).http://dx.doi.org/10.1155/2011/725494
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoling Han
Hongliang Gao
spellingShingle Xiaoling Han
Hongliang Gao
Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation
Mathematical Problems in Engineering
author_facet Xiaoling Han
Hongliang Gao
author_sort Xiaoling Han
title Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation
title_short Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation
title_full Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation
title_fullStr Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation
title_full_unstemmed Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation
title_sort positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2011-01-01
description By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation D0+αu(t)+λa(t)f(t,u(t))=0,  0<t<1,   u(0)=0,  u(1)=Σi=1∞αiu(ξi) are considered, where 1<α≤2 is a real number, λ is a positive parameter, D0+α is the standard Riemann-Liouville differentiation, and ξi∈(0,1), αi∈[0,∞) with Σi=1∞αiξiα-1<1, a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,∞),[0,∞)).
url http://dx.doi.org/10.1155/2011/725494
work_keys_str_mv AT xiaolinghan positivesolutionsofnonlineareigenvalueproblemsforanonlocalfractionaldifferentialequation
AT honglianggao positivesolutionsofnonlineareigenvalueproblemsforanonlocalfractionaldifferentialequation
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