Oscillation of higher order difference equations via comparison

Glasnik Matematicki, Vol. 39, No.2 (2004), 287-299.

OSCILLATION OF HIGHER ORDER DIFFERENCE EQUATIONS VIA COMPARISON

Ravi P. Agarwal, Said R. Grace and Donal O'Regan

R. P. Agarwal, Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, U.S.A.
e-mail: agarwal@fit.edu

S. R. Grace, Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt
e-mail: srgrace@eng.cu.edu.eg

D. O'Regan, Department of Mathematics, National University of Ireland, Galway, Ireland
e-mail: donal.oregan@nuigalway.ie

Abstract. In this paper we shall present some new oscillation criteria for difference equations of the form

Δ^m x(n) + q(n) f(x[n - τ]) = 0

and

Δ^m x(n) = q(t) f(x[n - τ]) + p(n) F(x[n + σ])

via comparison with some difference equations of lower order whose oscillatory behavior are known.

2000 Mathematics Subject Classification. 39A10.

Key words and phrases. Oscillation, nonoscillation, difference, nonlinear, comparison.

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