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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |