Geodesic
Iterative technique for a third-order three-point BVP with sign-changing Green's function
Electronic journal of differential equations, Tome 2013 (2013)
In this article, by applying iterative technique, we study the third-order three-point boundary value problem

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

where $f\in C([0,1]\times[0,+\infty),[0,+\infty))$ and $\eta\in[2-\sqrt{2},1)$. The emphasis is mainly that although the corresponding Green's function is sign-changing, the solution obtained is still positive. Moreover, our iterative scheme starts off with zero function, which implies that the iterative scheme is feasible. An example is also included to illustrate the main results.
Classification : 34B10, 34B18
Keywords: boundary value problem, Green's function, positive solution, existence of solutions, iterative technique 
@article{EJDE_2013__2013__a48,
     author = {Sun,  Jian-Ping and Zhao,  Juan},
     title = {Iterative technique for a third-order three-point {BVP} with sign-changing {Green's} function},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1294.34013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a48/}
}
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Sun,  Jian-Ping; Zhao,  Juan. Iterative technique for a third-order three-point BVP with sign-changing Green's function. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a48/