Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function
We are concerned with the following third-order boundary value problem with integral boundary condition: u′′′(t)=f(t,u(t)), t∈[0,1], u′(0)=u(1)=0, u′′(η)+∫αβu(t)dt=0, where 1/2<α≤β≤1, α+β≤4/3, and η∈(1/2,α]. Although the corresponding Green's function is sign-changing, we still obtain...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/491423 |
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| author | Bing-Wei Niu Jian-Ping Sun Qiu-Yan Ren |
| author_facet | Bing-Wei Niu Jian-Ping Sun Qiu-Yan Ren |
| author_sort | Bing-Wei Niu |
| collection | DOAJ |
| description | We are concerned with the following third-order boundary value problem with integral boundary condition: u′′′(t)=f(t,u(t)), t∈[0,1], u′(0)=u(1)=0, u′′(η)+∫αβu(t)dt=0, where 1/2<α≤β≤1, α+β≤4/3, and η∈(1/2,α]. Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained. |
| format | Article |
| id | doaj-art-d00623cf8c054e5c8f39940e7a5527c6 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-d00623cf8c054e5c8f39940e7a5527c62025-02-03T01:31:09ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/491423491423Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's FunctionBing-Wei Niu0Jian-Ping Sun1Qiu-Yan Ren2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaCollege of Technology and Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaWe are concerned with the following third-order boundary value problem with integral boundary condition: u′′′(t)=f(t,u(t)), t∈[0,1], u′(0)=u(1)=0, u′′(η)+∫αβu(t)dt=0, where 1/2<α≤β≤1, α+β≤4/3, and η∈(1/2,α]. Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained.http://dx.doi.org/10.1155/2015/491423 |
| spellingShingle | Bing-Wei Niu Jian-Ping Sun Qiu-Yan Ren Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function Journal of Function Spaces |
| title | Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function |
| title_full | Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function |
| title_fullStr | Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function |
| title_full_unstemmed | Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function |
| title_short | Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function |
| title_sort | two positive solutions of third order bvp with integral boundary condition and sign changing green s function |
| url | http://dx.doi.org/10.1155/2015/491423 |
| work_keys_str_mv | AT bingweiniu twopositivesolutionsofthirdorderbvpwithintegralboundaryconditionandsignchanginggreensfunction AT jianpingsun twopositivesolutionsofthirdorderbvpwithintegralboundaryconditionandsignchanginggreensfunction AT qiuyanren twopositivesolutionsofthirdorderbvpwithintegralboundaryconditionandsignchanginggreensfunction |