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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| Format: | Article |
| Language: | English |
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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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| author | S. Nageswara Rao M. Zico Meetei |
| author_facet | S. Nageswara Rao M. Zico Meetei |
| author_sort | S. Nageswara Rao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-47c74a582edf4372ac622a82a74d3a03 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-47c74a582edf4372ac622a82a74d3a032025-02-03T01:23:53ZengWileyInternational Journal of Differential Equations1687-96431687-96512019-01-01201910.1155/2019/28938572893857Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value ProblemsS. Nageswara Rao0M. Zico Meetei1Department of Mathematics, Jazan University, Jazan, Saudi ArabiaDepartment of Mathematics, Jazan University, Jazan, Saudi ArabiaIn 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.http://dx.doi.org/10.1155/2019/2893857 |
| spellingShingle | S. Nageswara Rao M. Zico Meetei Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems International Journal of Differential Equations |
| title | Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems |
| title_full | Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems |
| title_fullStr | Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems |
| title_full_unstemmed | Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems |
| title_short | Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems |
| title_sort | positive solutions for a coupled system of nonlinear semipositone fractional boundary value problems |
| url | http://dx.doi.org/10.1155/2019/2893857 |
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