 
Summary: International Journal of Nonlinear Differential Equations
7:12 (2002) 97104.
EIGENVALUE INTERVALS FOR A SECONDORDER
MIXEDCONDITIONS PROBLEM ON TIME SCALES
DOUGLAS R. ANDERSON
Abstract. We study the existence of eigenvalue intervals for the secondorder
dynamic equation on time scales, x
(t)+q(t)f(x(t)) = 0, t [a, b] satisfying the
boundary conditions x((a))  x
((a)) = 0 and x(b) + x
(b) = 0, where f
is a positive function and q is a nonnegative function that is allowed to vanish on
some subintervals of [(a), b] of the time scale. The methods involve applications of
a fixedpoint theorem for operators on a cone in a Banach space.
1. introduction
One goal as the result of Hilger's [21] initial paper introducing time scales has
been the unification of the continuous and discrete calculus, and then the extension
of those results to dynamic equations on time scales. Some other early papers in this
area include Agarwal and Bohner [1], Atici and Guseinov [7], Aulbach and Hilger [8],
and Erbe and Hilger [15]. For an excellent introduction to the overall area of dynamic
