 
Summary: Electronic Journal of Differential Equations, Vol. 2007(2007), No. 107, pp. 115.
ISSN: 10726691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu (login: ftp)
EXISTENCE OF SOLUTIONS TO A THIRDORDER
MULTIPOINT PROBLEM ON TIME SCALES
DOUGLAS R. ANDERSON AND JOAN HOFFACKER
Abstract. We are concerned with the existence and form of solutions to
nonlinear thirdorder threepoint and multipoint boundaryvalue problems
on general time scales. Using the corresponding Green function, we prove
the existence of at least one positive solution using the GuoKrasnosel'skii
fixed point theorem. Moreover, a thirdorder multipoint eigenvalue problem
is formulated, and eigenvalue intervals for the existence of a positive solution
are found.
1. introduction
We will establish the corresponding Green function whereby conditions can be
given such that a positive solution exists for the following nonlinear thirdorder
threepoint boundary value problem on arbitrary time scales
(px
) (t) + a(t)f(x(t)) = 0, t [t1, t3]T, (1.1)
x((t1)) = x
