 
Summary: Applicable Analysis and Discrete Mathematics
available online at http://pefmath.etf.bg.ac.yu
Appl. Anal. Discrete Math. 4 (2010), 338346. doi:10.2298/AADM100514024A
STURMPICONE COMPARISON THEOREM FOR
MATRIX SYSTEMS ON TIME SCALES
Douglas R. Anderson, John R. Graef
A wellknown Picone identity is extended and generalized to secondorder
dynamic matrix equations on arbitrary time scales. A comparison theorem
is obtained in the spirit of the classical SturmPicone comparison theorem
that extends known scalar results to matrix equations that include the lin
ear homogeneous and inhomogeneous cases, and nonlinear unperturbed and
perturbed cases.
1. INTRODUCTION
More than 170 years have past since Sturm [18] published his famous com
parison theorem for second order linear differential equations. There is reason to
believe that in fact he first proved this result for difference equations (see Reid
[17]). The first nonlinear version of the SturmPicone identity and comparison
theorem appeared in Graef and Spikes [12] for second order ordinary differential
equations. Jaros and Kusano extended the identity to second order halflinear
equations in [15]. Sturm type comparison theorems for higher order difference
