 
Summary: Electronic Journal of Differential Equations, Vol. 2009(2009), No. 24, pp. 113.
ISSN: 10726691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu
OSCILLATION AND NONOSCILLATION CRITERIA FOR
TWODIMENSIONAL TIMESCALE SYSTEMS OF
FIRSTORDER NONLINEAR DYNAMIC EQUATIONS
DOUGLAS R. ANDERSON
Abstract. Oscillation criteria for twodimensional difference and differential
systems of firstorder linear difference equations are generalized and extended
to nonlinear dynamic equations on arbitrary time scales. This unifies and
extends under one theory previous linear results from discrete and continuous
systems. An example is given illustrating that a key theorem is sharp on all
time scales.
1. prelude
Jiang and Tang [14] establish sufficient conditions for the oscillation of the linear
twodimensional difference system
xn = pnyn, yn1 = qnxn, n Z, (1.1)
where {pn}, {qn} are nonnegative real sequences and is the forward difference
operator given via xn = xn+1  xn; see also Li [16]. The system (1.1) may be
viewed as a discrete analogue of the differential system
