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Applicable Analysis and Discrete Mathematics available online at http://pefmath.etf.bg.ac.yu
 

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
STURM-PICONE COMPARISON THEOREM FOR
MATRIX SYSTEMS ON TIME SCALES
Douglas R. Anderson, John R. Graef
A well-known Picone identity is extended and generalized to second-order
dynamic matrix equations on arbitrary time scales. A comparison theorem
is obtained in the spirit of the classical Sturm-Picone 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 Sturm-Picone 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 half-linear
equations in [15]. Sturm type comparison theorems for higher order difference

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics