Summary: Dynamic Systems and Applications 12:1-2 (2003) 9-22
GREEN'S FUNCTION FOR AN EVEN ORDER MIXED
DERIVATIVE PROBLEM ON TIME SCALES
DOUGLAS R. ANDERSON AND JOAN HOFFACKER
Abstract. Concordia College, Department of Mathematics and Computer
Science, Moorhead, MN 56562 USA. E-mail: email@example.com
University of Georgia, Department of Mathematics, Athens, GA 30602 USA.
ABSTRACT. Green's function for an even-order focal problem, where the derivatives alternate
between nabla and delta derivatives, is found, and several examples are given for standard time
scales. The signs of the function and its derivatives are determined, and whether a symmetry
condition holds for an arbitrary time scale is also discussed. The results are then applied to give
existence criteria for a positive solution to a nonlinear boundary-value problem.
AMS (MOS) Subject Classification. 39A10, 34B10.
A time scale T is an arbitrary nonempty closed subset of the reals R , . We define the sets T
and T by