On the solvability of third-order three points systems of differential equations with dependence on the first derivatives
This paper presents sufficient conditions for the solvability of the third order three point boundary value problem -u′′′(t)=f(t,v(t),v′(t)) -v′′′(t)=h(t,u(t),u′(t)) u(0)=u′(0)=0,u′(1)=αu′(η) v(0)=v′(0)=0,v′(1)=αv′(η). The arguments apply Green's function associated to the linear problem and th...
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| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2018
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| Texto completo: | http://hdl.handle.net/10174/21885 |
| País: | Portugal |
| Oai: | oai:dspace.uevora.pt:10174/21885 |
| Resumo: | This paper presents sufficient conditions for the solvability of the third order three point boundary value problem -u′′′(t)=f(t,v(t),v′(t)) -v′′′(t)=h(t,u(t),u′(t)) u(0)=u′(0)=0,u′(1)=αu′(η) v(0)=v′(0)=0,v′(1)=αv′(η). The arguments apply Green's function associated to the linear problem and the Guo--Krasnosel'skiĭ theorem of compression-expansion cones. The dependence on the first derivatives is overcome by the construction of an adequate cone and suitable conditions of superlinearity/sublinearity near 0 and +∞. Last section contains an example to illustrate the applicability of the theorem. |
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