Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter
In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions: D0α+u(t) +h(t)f(t,u(t)) = 0, 0<t<1, u(0) = u′(0) = u″(0) = 0, u(1) = λ∫0ηu(s)ds, where 3 < α ≤ 4,0 < η ≤ 1, 0 -< ληαα <1, D0+...
| Main Authors: | , , |
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| Format: | Journal Article |
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Elsevier Inc.
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/31431 |
| _version_ | 1848753378907127808 |
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| author | Zhang, X. Wang, L. Sun, Qian |
| author_facet | Zhang, X. Wang, L. Sun, Qian |
| author_sort | Zhang, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions: D0α+u(t) +h(t)f(t,u(t)) = 0, 0<t<1, u(0) = u′(0) = u″(0) = 0, u(1) = λ∫0ηu(s)ds, where 3 < α ≤ 4,0 < η ≤ 1, 0 -< ληαα <1, D0+α is the standard Riemann–Liouville derivative. h(t) is allowed to be singular at t=0 and t=1. By using the properties of the Green function, u0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator, we obtain some existence results of positive solution. |
| first_indexed | 2025-11-14T08:23:34Z |
| format | Journal Article |
| id | curtin-20.500.11937-31431 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:23:34Z |
| publishDate | 2014 |
| publisher | Elsevier Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-314312017-09-13T15:19:35Z Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter Zhang, X. Wang, L. Sun, Qian Positive solution Fixed point theorem Green’s function Integral boundary conditions Fractional differential equation In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions: D0α+u(t) +h(t)f(t,u(t)) = 0, 0<t<1, u(0) = u′(0) = u″(0) = 0, u(1) = λ∫0ηu(s)ds, where 3 < α ≤ 4,0 < η ≤ 1, 0 -< ληαα <1, D0+α is the standard Riemann–Liouville derivative. h(t) is allowed to be singular at t=0 and t=1. By using the properties of the Green function, u0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator, we obtain some existence results of positive solution. 2014 Journal Article http://hdl.handle.net/20.500.11937/31431 10.1016/j.amc.2013.10.089 Elsevier Inc. restricted |
| spellingShingle | Positive solution Fixed point theorem Green’s function Integral boundary conditions Fractional differential equation Zhang, X. Wang, L. Sun, Qian Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter |
| title | Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter |
| title_full | Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter |
| title_fullStr | Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter |
| title_full_unstemmed | Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter |
| title_short | Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter |
| title_sort | existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter |
| topic | Positive solution Fixed point theorem Green’s function Integral boundary conditions Fractional differential equation |
| url | http://hdl.handle.net/20.500.11937/31431 |