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Summary: SECOND-ORDER n-POINT 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
second-order Sturm-Liouville-type 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 Guo-Krasnosel'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 second-order multipoint time-scale eigenvalue problem
py
(t)- q(t)y(t)+h(t) f (y) = 0, t1 < t < tn, (1.1)
y t1 - p t1 y
t1 =
n-1
i=2
ai y ti , y tn +p tn y
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