Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 19, pp. 1-21.

Title: Existence and uniqueness of solutions to a super-linear 
       three-point boundary-value problem

Authors: Bruce Calvert (University of Auckland, New Zealand)
         Chaitan P. Gupta (University of Nevada, Reno, NV, USA)
 
Abstract: 
 In previous papers, degree theory for nonlinear operators has 
 been used to study a class of three-point boundary-value problems
 for second order ordinary differential equations having a 
 super-linear term, and existence of a sequence of solutions has 
 been shown. In this paper, we forgo the  previous approach for 
 the shooting method, which gives a drastically  simpler existence 
 theory, with less assumptions, and easy calculation  of solutions.
 We even obtain uniqueness in the simplest case.
 
Submitted November 16, 2004. Published February 7, 2005.
Math Subject Classifications: 34B10, 34B15.
Key Words: Super-linear; three-point boundary-value problem.