Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives
We study the existence of positive solutions for the system of nonlinear semipositone boundary value problems with Riemann-Liouville fractional derivatives D0+αD0+αu=f1t,u,u′,v,v′, 0<t<1, D0+αD0+αv=f2(t,u,u′,v,v′), 0<t<1, u0=u′0=u′(1)=D0+αu(0)=D0+α+1u(0)=D0+α+1u(1)=0, and v(0)=v′(0)=v′...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/7351653 |
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| author | Xiaowei Qiu Jiafa Xu Donal O’Regan Yujun Cui |
| author_facet | Xiaowei Qiu Jiafa Xu Donal O’Regan Yujun Cui |
| author_sort | Xiaowei Qiu |
| collection | DOAJ |
| description | We study the existence of positive solutions for the system of nonlinear semipositone boundary value problems with Riemann-Liouville fractional derivatives D0+αD0+αu=f1t,u,u′,v,v′, 0<t<1, D0+αD0+αv=f2(t,u,u′,v,v′), 0<t<1, u0=u′0=u′(1)=D0+αu(0)=D0+α+1u(0)=D0+α+1u(1)=0, and v(0)=v′(0)=v′(1)=D0+αv(0)=D0+α+1v(0)=D0+α+1v(1)=0, where α∈(2,3] is a real number and D0+α is the standard Riemann-Liouville fractional derivative of order α. Under some appropriate conditions for semipositone nonlinearities, we use the fixed point index to establish two existence theorems. Moreover, nonnegative concave and convex functions are used to depict the coupling behavior of our nonlinearities. |
| format | Article |
| id | doaj-art-68d71377af084fa899be12ec66310d30 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-68d71377af084fa899be12ec66310d302025-02-03T01:31:39ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/73516537351653Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional DerivativesXiaowei Qiu0Jiafa Xu1Donal O’Regan2Yujun Cui3School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, ChinaSchool of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, ChinaSchool of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, IrelandState Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, ChinaWe study the existence of positive solutions for the system of nonlinear semipositone boundary value problems with Riemann-Liouville fractional derivatives D0+αD0+αu=f1t,u,u′,v,v′, 0<t<1, D0+αD0+αv=f2(t,u,u′,v,v′), 0<t<1, u0=u′0=u′(1)=D0+αu(0)=D0+α+1u(0)=D0+α+1u(1)=0, and v(0)=v′(0)=v′(1)=D0+αv(0)=D0+α+1v(0)=D0+α+1v(1)=0, where α∈(2,3] is a real number and D0+α is the standard Riemann-Liouville fractional derivative of order α. Under some appropriate conditions for semipositone nonlinearities, we use the fixed point index to establish two existence theorems. Moreover, nonnegative concave and convex functions are used to depict the coupling behavior of our nonlinearities.http://dx.doi.org/10.1155/2018/7351653 |
| spellingShingle | Xiaowei Qiu Jiafa Xu Donal O’Regan Yujun Cui Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives Journal of Function Spaces |
| title | Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives |
| title_full | Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives |
| title_fullStr | Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives |
| title_full_unstemmed | Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives |
| title_short | Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives |
| title_sort | positive solutions for a system of nonlinear semipositone boundary value problems with riemann liouville fractional derivatives |
| url | http://dx.doi.org/10.1155/2018/7351653 |
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