Multiple Solutions to Fractional Difference Boundary Value Problems
The following fractional difference boundary value problems ▵νyt=-ft+ν-1,yt+ν-1, y(ν-2)=y(ν+b+1)=0 are considered, where 1<ν≤2 is a real number and ▵νy(t) is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establis...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/879380 |
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| author | Huiqin Chen Yaqiong Cui Xianglan Zhao |
| author_facet | Huiqin Chen Yaqiong Cui Xianglan Zhao |
| author_sort | Huiqin Chen |
| collection | DOAJ |
| description | The following fractional difference boundary value problems ▵νyt=-ft+ν-1,yt+ν-1, y(ν-2)=y(ν+b+1)=0 are considered, where 1<ν≤2 is a real number and ▵νy(t) is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions on f which are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. Our results significantly improve and generalize those in the literature. A number of examples are given to illustrate our main results. |
| format | Article |
| id | doaj-art-3d6f0eff9b3847dfb46a2463668a5dde |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3d6f0eff9b3847dfb46a2463668a5dde2025-02-03T06:11:31ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/879380879380Multiple Solutions to Fractional Difference Boundary Value ProblemsHuiqin Chen0Yaqiong Cui1Xianglan Zhao2School of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037009, ChinaSchool of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037009, ChinaSchool of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037009, ChinaThe following fractional difference boundary value problems ▵νyt=-ft+ν-1,yt+ν-1, y(ν-2)=y(ν+b+1)=0 are considered, where 1<ν≤2 is a real number and ▵νy(t) is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions on f which are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. Our results significantly improve and generalize those in the literature. A number of examples are given to illustrate our main results.http://dx.doi.org/10.1155/2014/879380 |
| spellingShingle | Huiqin Chen Yaqiong Cui Xianglan Zhao Multiple Solutions to Fractional Difference Boundary Value Problems Abstract and Applied Analysis |
| title | Multiple Solutions to Fractional Difference Boundary Value Problems |
| title_full | Multiple Solutions to Fractional Difference Boundary Value Problems |
| title_fullStr | Multiple Solutions to Fractional Difference Boundary Value Problems |
| title_full_unstemmed | Multiple Solutions to Fractional Difference Boundary Value Problems |
| title_short | Multiple Solutions to Fractional Difference Boundary Value Problems |
| title_sort | multiple solutions to fractional difference boundary value problems |
| url | http://dx.doi.org/10.1155/2014/879380 |
| work_keys_str_mv | AT huiqinchen multiplesolutionstofractionaldifferenceboundaryvalueproblems AT yaqiongcui multiplesolutionstofractionaldifferenceboundaryvalueproblems AT xianglanzhao multiplesolutionstofractionaldifferenceboundaryvalueproblems |