Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators
This paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,...
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/9563791 |
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| author | Chen Yang Xiaolin Zhu |
| author_facet | Chen Yang Xiaolin Zhu |
| author_sort | Chen Yang |
| collection | DOAJ |
| description | This paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,2, βi∈3,4, D0+αi and D0+βi are the standard Riemann-Liouville derivatives, φpis=spi−2s,pi>1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈0,1,bi∈0,ηi1−αi/pi−1, i=1,2, and f,g∈C0,1×0,+∞×0,+∞,0,+∞ and λ and μ are two positive parameters. We obtain the existence and uniqueness of positive solutions depending on parameters for the system by utilizing a recent fixed point theorem. Furthermore, an example is present to illustrate our main result. |
| format | Article |
| id | doaj-art-06249d4ba75d46459063183a74b4b2e7 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-06249d4ba75d46459063183a74b4b2e72025-02-03T01:04:29ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/95637919563791Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian OperatorsChen Yang0Xiaolin Zhu1Basic Course Department, Business College of Shanxi University, Taiyuan, Shanxi 030031, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, 030006 Shanxi, ChinaThis paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,2, βi∈3,4, D0+αi and D0+βi are the standard Riemann-Liouville derivatives, φpis=spi−2s,pi>1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈0,1,bi∈0,ηi1−αi/pi−1, i=1,2, and f,g∈C0,1×0,+∞×0,+∞,0,+∞ and λ and μ are two positive parameters. We obtain the existence and uniqueness of positive solutions depending on parameters for the system by utilizing a recent fixed point theorem. Furthermore, an example is present to illustrate our main result.http://dx.doi.org/10.1155/2020/9563791 |
| spellingShingle | Chen Yang Xiaolin Zhu Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators Advances in Mathematical Physics |
| title | Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators |
| title_full | Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators |
| title_fullStr | Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators |
| title_full_unstemmed | Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators |
| title_short | Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators |
| title_sort | positive solutions depending on parameters for a nonlinear fractional system with p laplacian operators |
| url | http://dx.doi.org/10.1155/2020/9563791 |
| work_keys_str_mv | AT chenyang positivesolutionsdependingonparametersforanonlinearfractionalsystemwithplaplacianoperators AT xiaolinzhu positivesolutionsdependingonparametersforanonlinearfractionalsystemwithplaplacianoperators |