Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs
We are concerned with the following system of third-order three-point boundary value problems: u′′′(t)+f(t,v(t))=0, t∈(0,1), v′′′(t)+g(t,u(t))=0, t∈(0,1), u(0)=u′′(0)=0, u′(1)=αu(η), v(0)=v′′(0)=0, and v′(1)=αv(η), where 0<η<1 and 0<α<1/η. By imposing some suitable conditions on f and g,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/6874643 |
| Summary: | We are concerned with the following system of third-order three-point boundary value problems: u′′′(t)+f(t,v(t))=0, t∈(0,1), v′′′(t)+g(t,u(t))=0, t∈(0,1), u(0)=u′′(0)=0, u′(1)=αu(η), v(0)=v′′(0)=0, and v′(1)=αv(η), where 0<η<1 and 0<α<1/η. By imposing some suitable conditions on f and g, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index. |
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| ISSN: | 2314-8896 2314-8888 |