Electron. J. Diff. Eqns., Vol. 2004(2004), No. 47, pp. 1-12.

Nonlinear triple-point problems on time scales

Douglas R. Anderson

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 $\beta+\gamma>0$, $0 less than \alpha less than \frac{c-a}{c-b}$ 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.

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Douglas R. Anderson
Department of Mathematics and Computer Science
Concordia College, Moorhead, Minnesota 56562, USA
email: andersod@cord.edu

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