Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 215, pp. 1-9.

Title: Iterative technique for a third-order three-point BVP with
       sign-changing Green's function.

Authors: Jian-Ping Sun (Lanzhou Univ. of Technology, Gansu, China)
         Juan Zhao     (Lanzhou Univ. of Technology, Gansu, China)

Abstract:
 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.

Submitted July 5, 2013. Published September 30, 2013.
Math Subject Classifications: 34B10, 34B18.
Key Words: Boundary value problem; Green's function;  positive solution; 
           existence of solutions; iterative technique.