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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/817542 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850213822477893632 |
|---|---|
| author | Chengbo Zhai Mengru Hao |
| author_facet | Chengbo Zhai Mengru Hao |
| author_sort | Chengbo Zhai |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-879e129d7d58443c8f365f1369148a4e |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-879e129d7d58443c8f365f1369148a4e2025-08-20T02:09:03ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/817542817542Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential EquationsChengbo Zhai0Mengru Hao1School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaBy 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.http://dx.doi.org/10.1155/2014/817542 |
| spellingShingle | Chengbo Zhai Mengru Hao Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations The Scientific World Journal |
| title | Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations |
| title_full | Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations |
| title_fullStr | Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations |
| title_full_unstemmed | Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations |
| title_short | Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations |
| title_sort | multiple positive solutions to nonlinear boundary value problems of a system for fractional differential equations |
| url | http://dx.doi.org/10.1155/2014/817542 |
| work_keys_str_mv | AT chengbozhai multiplepositivesolutionstononlinearboundaryvalueproblemsofasystemforfractionaldifferentialequations AT mengruhao multiplepositivesolutionstononlinearboundaryvalueproblemsofasystemforfractionaldifferentialequations |