Geodesic
Existence of solutions to a third-order multi-point problem on time scales
Electronic journal of differential equations, Tome 2007 (2007)
We are concerned with the existence and form of solutions to nonlinear third-order three-point and multi-point boundary-value problems on general time scales. Using the corresponding Green function, we prove the existence of at least one positive solution using the Guo-Krasnosel'skii fixed point theorem. Moreover, a third-order multi-point eigenvalue problem is formulated, and eigenvalue intervals for the existence of a positive solution are found.
Classification : 34B18, 34B27, 34B10, 39A10
Keywords: boundary value problem, time scale, third order, Green function 
@article{EJDE_2007__2007__a67,
     author = {Anderson,  Douglas R. and Hoffacker,  Joan},
     title = {Existence of solutions to a third-order multi-point problem on time scales},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1138.34305},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a67/}
}
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%A Hoffacker,  Joan
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%J Electronic journal of differential equations
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Anderson,  Douglas R.; Hoffacker,  Joan. Existence of solutions to a third-order multi-point problem on time scales. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a67/