Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations
By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D0+ν1y1(t)=λ1a1(t)f(y1(t),y2(t)), -D0+ν2y2(t)=λ2a2(t)g(y1(t),y2(t)), where D0+ν is the standard Riemann-Liouville fractiona...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/817542 |
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| Summary: | By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D0+ν1y1(t)=λ1a1(t)f(y1(t),y2(t)), -D0+ν2y2(t)=λ2a2(t)g(y1(t),y2(t)), where D0+ν is the standard Riemann-Liouville fractional derivative, ν1,ν2∈(n-1,n] for n>3 and n∈N, subject to the boundary conditions y1(i)(0)=0=y2(i)(0), for 0≤i≤n-2, and [D0+αy1(t)]t=1=0=[D0+αy2(t)]t=1, for 1≤α≤n-2, or y1(i)(0)=0=y2(i)(0), for 0≤i≤n-2, and [D0+αy1(t)]t=1=ϕ1(y1), [D0+αy2(t)]t=1=ϕ2(y2), for 1≤α≤n-2, ϕ1,ϕ2∈C([0,1],R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result. |
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| ISSN: | 2356-6140 1537-744X |