Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 17, pp. 1-14.

Title: Positive solutions to a generalized second-order  
       three-point boundary-value problem on time scales

Authors: Hua Luo (Northwest Normal Univ., Gansu, China)
         Qiaozhen Ma (Northwest Normal Univ., Gansu, China)
 
Abstract: 
 Let $\mathbb{T}$ be a time scale with $0,T \in \mathbb{T}$. We
 investigate the existence and multiplicity of positive solutions
 to the nonlinear second-order three-point boundary-value problem
 $$\displaylines{
 u^{\Delta\nabla}(t)+a(t)f(u(t))=0,\quad t\in[0, T]\subset \mathbb{T},\cr
 u(0)=\beta u(\eta),\quad u(T)=\alpha u(\eta)
 }$$
 on time scales $\mathbb{T}$, where $0<\eta<T$,
 $0<\alpha<\frac{T}{\eta}$, $0<\beta<\frac{T-\alpha\eta}{T-\eta}$
 are given constants.
 
Submitted September 1, 2004. Published February 1, 2005.
Math Subject Classifications: 34B18, 39A10
Key Words: Time scales; three-point boundary value problems; cone; 
           fixed points; positive solutions.