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Electronic Journal of Differential Equations, Vol. 2009(2009), No. 24, pp. 113. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
 

Summary: Electronic Journal of Differential Equations, Vol. 2009(2009), No. 24, pp. 113.
ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu
OSCILLATION AND NONOSCILLATION CRITERIA FOR
TWO-DIMENSIONAL TIME-SCALE SYSTEMS OF
FIRST-ORDER NONLINEAR DYNAMIC EQUATIONS
DOUGLAS R. ANDERSON
Abstract. Oscillation criteria for two-dimensional difference and differential
systems of first-order 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
two-dimensional difference system
xn = pnyn, yn-1 = -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

  

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

 

Collections: Mathematics