Geodesic
Multiple positive solutions for a third-order three-point BVP with sign-changing Green's function
Electronic journal of differential equations, Tome 2012 (2012)
This article concerns the third-order three-point boundary-value problem

$\displaylines{ u'''(t)=f(t,u(t)),\quad t\in [0,1], \cr u'(0)=u(1)=u''(\eta)=0. }$

Although the corresponding Green's function is sign-changing, we still obtain the existence of at least 2m-1 positive solutions for arbitrary positive integer m under suitable conditions on f.
Classification : 34B10, 34B18
Keywords: third-order three-point boundary-value problem, sign-changing Green's function, positive solution 
@article{EJDE_2012__2012__a64,
     author = {Sun,  Jian-Ping and Zhao,  Juan},
     title = {Multiple positive solutions for a third-order three-point {BVP} with sign-changing {Green's} function},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1260.34049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a64/}
}
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%A Zhao,  Juan
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%F EJDE_2012__2012__a64
Sun,  Jian-Ping; Zhao,  Juan. Multiple positive solutions for a third-order three-point BVP with sign-changing Green's function. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a64/