Geodesic
Third-order nonlocal problems with sign-changing nonlinearity on time scales
Electronic journal of differential equations, Tome 2007 (2007)
We are concerned with the existence and form of positive solutions to a nonlinear third-order three-point nonlocal boundary-value problem on general time scales. Using Green's functions, we prove the existence of at least one positive solution using the Guo-Krasnoselskii fixed point theorem. Due to the fact that the nonlinearity is allowed to change sign in our formulation, and the novelty of the boundary conditions, these results are new for discrete, continuous, quantum and arbitrary time scales.
Classification : 34B27, 34B10, 39A10
Keywords: boundary value problem, time scale, three-point, Green's function 
@article{EJDE_2007__2007__a151,
     author = {Anderson,  Douglas R. and Tisdell,  Christopher C.},
     title = {Third-order nonlocal problems with sign-changing nonlinearity on time scales},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1121.34031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a151/}
}
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%A Tisdell,  Christopher C.
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%J Electronic journal of differential equations
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%V 2007
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%F EJDE_2007__2007__a151
Anderson,  Douglas R.; Tisdell,  Christopher C. Third-order nonlocal problems with sign-changing nonlinearity on time scales. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a151/