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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2011-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2011/725494 |
| Summary: | 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,∞)). |
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| ISSN: | 1024-123X 1563-5147 |