Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems
In this paper, we consider a four-point coupled boundary value problem for system of the nonlinear semipositone fractional differential equation D0+αu(t)+λf(t,u(t),v(t))=0, 0<t<1, D0+αv(t)+μg(t,u(t),v(t))=0, 0<t<1, u(0)=v(0)=0, a1D0+βu(1)=b1D0+βv(ξ), a2D0+βv(1)=b2D0+βu(η), η,ξ∈(0,1),...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2019/2893857 |
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| Summary: | In this paper, we consider a four-point coupled boundary value problem for system of the nonlinear semipositone fractional differential equation D0+αu(t)+λf(t,u(t),v(t))=0, 0<t<1, D0+αv(t)+μg(t,u(t),v(t))=0, 0<t<1, u(0)=v(0)=0, a1D0+βu(1)=b1D0+βv(ξ), a2D0+βv(1)=b2D0+βu(η), η,ξ∈(0,1), where the coefficients ai,bi,i=1,2 are real positive constants, α∈(1,2],β∈(0,1],D0+α, D0+β are the standard Riemann-Liouville derivatives. Values of the parameters λ and μ are determined for which boundary value problem has positive solution by utilizing a fixed point theorem on cone. |
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| ISSN: | 1687-9643 1687-9651 |