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.