The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems
We study the existence of solutions for the boundary value problem -Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)), -Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)), y1(ν-2)=Δy1(ν+b)=0, y2(μ-2)=Δy2(μ+b)=0, where 1<μ,ν≤2, f,g:R×R→R are continuous functions, b∈N0. The existence of solutions to this problem is established by the Gu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/707631 |
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| author | Yuanyuan Pan Zhenlai Han Shurong Sun Yige Zhao |
| author_facet | Yuanyuan Pan Zhenlai Han Shurong Sun Yige Zhao |
| author_sort | Yuanyuan Pan |
| collection | DOAJ |
| description | We study the existence of solutions for the boundary value problem -Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)), -Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)), y1(ν-2)=Δy1(ν+b)=0, y2(μ-2)=Δy2(μ+b)=0, where 1<μ,ν≤2, f,g:R×R→R are continuous functions, b∈N0. The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results. |
| format | Article |
| id | doaj-art-d7c071764d134ae1b039877ac80e2eb6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d7c071764d134ae1b039877ac80e2eb62025-02-03T05:58:07ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/707631707631The Existence of Solutions to a System of Discrete Fractional Boundary Value ProblemsYuanyuan Pan0Zhenlai Han1Shurong Sun2Yige Zhao3School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaWe study the existence of solutions for the boundary value problem -Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)), -Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)), y1(ν-2)=Δy1(ν+b)=0, y2(μ-2)=Δy2(μ+b)=0, where 1<μ,ν≤2, f,g:R×R→R are continuous functions, b∈N0. The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.http://dx.doi.org/10.1155/2012/707631 |
| spellingShingle | Yuanyuan Pan Zhenlai Han Shurong Sun Yige Zhao The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems Abstract and Applied Analysis |
| title | The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems |
| title_full | The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems |
| title_fullStr | The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems |
| title_full_unstemmed | The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems |
| title_short | The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems |
| title_sort | existence of solutions to a system of discrete fractional boundary value problems |
| url | http://dx.doi.org/10.1155/2012/707631 |
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