Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 47, pp. 1-12.

Title: Nonlinear triple-point problems on time scales
       
Author: Douglas R. Anderson (Concordia College, Moorhead, Minnesota, USA)

Abstract: 
 We establish the existence of multiple positive solutions to the
  nonlinear second-order triple-point boundary-value problem on
  time scales,
 $$\displaylines{
 u^{\Delta\nabla}(t)+h(t)f(t,u(t))=0, \cr
 u(a)=\alpha u(b)+\delta u^\Delta(a),\quad  
 \beta u(c)+\gamma u^\Delta(c)=0
 }$$
 for $t\in[a,c]\subset\mathbb{T}$, where $\mathbb{T}$ is a time scale,
 $\beta, \gamma, \delta\ge 0$ with $\beta+\gamma>0$,
 $0<\alpha<\frac{c-a}{c-b}$ and $b\in(a,c)\subset\mathbb{T}$.
  
Submitted March 7, 2004. Published April 6, 2004.
Math Subject Classifications: 34B10, 34B15, 39A10.
Key Words: Fixed-point theorems; time scales; dynamic equations; cone.