 
Summary: SECONDORDER nPOINT EIGENVALUE PROBLEMS
ON TIME SCALES
DOUGLAS R. ANDERSON AND RUYUN MA
Received 10 December 2004; Revised 3 November 2005; Accepted 6 November 2005
We discuss conditions for the existence of at least one positive solution to a nonlinear
secondorder SturmLiouvilletype multipoint eigenvalue problem on time scales. The
results extend previous work on both the continuous case and more general time scales,
and are based on the GuoKrasnosel'skii fixed point theorem.
Copyright © 2006 D. R. Anderson and R. Ma. This is an open access article distributed
under the Creative Commons Attribution License, which permits unrestricted use, dis
tribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction
We are interested in the secondorder multipoint timescale eigenvalue problem
py
(t) q(t)y(t)+h(t) f (y) = 0, t1 < t < tn, (1.1)
y t1  p t1 y
t1 =
n1
i=2
ai y ti , y tn +p tn y
