Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 118, pp. 1-7.

Title: Multiple positive solutions 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:
 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.

Submitted May 29, 2012. Published July 14, 2012.
Math Subject Classifications: 34B10, 34B18.
Key Words: Third-order three-point boundary-value problem; 
           sign-changing Green's function; positive solution