 
Summary: Electronic Journal of Differential Equations, Vol. 2007(2007), No. 19, pp. 112.
ISSN: 10726691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu (login: ftp)
THIRDORDER NONLOCAL PROBLEMS WITH
SIGNCHANGING NONLINEARITY ON TIME SCALES
DOUGLAS R. ANDERSON, CHRISTOPHER C. TISDELL
Abstract. We are concerned with the existence and form of positive solutions
to a nonlinear thirdorder threepoint nonlocal boundaryvalue problem on
general time scales. Using Green's functions, we prove the existence of at least
one positive solution using the GuoKrasnoselskii fixed point theorem. Due
to the fact that the nonlinearity is allowed to change sign in our formulation,
and the novelty of the boundary conditions, these results are new for discrete,
continuous, quantum and arbitrary time scales.
1. Statement of the problem
We will develop an interval of values whereby a positive solution exists for the
following nonlinear, thirdorder, threepoint, nonlocal boundaryvalue problem on
arbitrary time scales
(px
) (t) = f(t, x(t)), t [t1, t3]T, (1.1)
x((t1))  x
