The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications
We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t)+f(t,u(t))+e(t)=0,0<t<1,u(0)=u'(0)=⋯=u(n-2)(0)=0,u(1)=βu(η), where n-1<α≤n,n≥3,0<β≤1,0≤η≤1, D0+α is the standard Riemann-Liouville derivative. Here our n...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/531038 |
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| Summary: | We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t)+f(t,u(t))+e(t)=0,0<t<1,u(0)=u'(0)=⋯=u(n-2)(0)=0,u(1)=βu(η), where n-1<α≤n,n≥3,0<β≤1,0≤η≤1, D0+α is the standard Riemann-Liouville derivative. Here our nonlinearity f may be singular at u=0. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem. |
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| ISSN: | 1085-3375 1687-0409 |