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