Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments
We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and η∈(0,1), where Dα is the standard Riemann-Liouville derivat...
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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/10.1155/2014/158436 |
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| author | Zhaocai Hao Yubo Huang |
| author_facet | Zhaocai Hao Yubo Huang |
| author_sort | Zhaocai Hao |
| collection | DOAJ |
| description | We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and η∈(0,1), where Dα is the standard Riemann-Liouville derivative, f:[0,∞)→[0,∞) is continuous, f(0)>0, h :[0,1]→(−∞,+∞), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results. |
| format | Article |
| id | doaj-art-80a7ec9ba9f64a0ab18640066cb20784 |
| 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-80a7ec9ba9f64a0ab18640066cb207842025-02-03T06:08:25ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/158436158436Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced ArgumentsZhaocai Hao0Yubo Huang1School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, ChinaWe discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and η∈(0,1), where Dα is the standard Riemann-Liouville derivative, f:[0,∞)→[0,∞) is continuous, f(0)>0, h :[0,1]→(−∞,+∞), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.http://dx.doi.org/10.1155/2014/158436 |
| spellingShingle | Zhaocai Hao Yubo Huang Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments Abstract and Applied Analysis |
| title | Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments |
| title_full | Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments |
| title_fullStr | Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments |
| title_full_unstemmed | Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments |
| title_short | Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments |
| title_sort | existence of positive solutions to nonlinear fractional boundary value problem with changing sign nonlinearity and advanced arguments |
| url | http://dx.doi.org/10.1155/2014/158436 |
| work_keys_str_mv | AT zhaocaihao existenceofpositivesolutionstononlinearfractionalboundaryvalueproblemwithchangingsignnonlinearityandadvancedarguments AT yubohuang existenceofpositivesolutionstononlinearfractionalboundaryvalueproblemwithchangingsignnonlinearityandadvancedarguments |