Oscillatory and asymptotic properties of solutions of nonlinear fourth order difference equations

Glasnik Matematicki, Vol. 37, No.1 (2002), 119-131.

OSCILLATORY AND ASYMPTOTIC PROPERTIES OF SOLUTIONS OF NONLINEAR FOURTH ORDER DIFFERENCE EQUATIONS

E. Thandapani and I. M. Arockiasamy

Department of Mathematics, Periyar University, Salem - 636011, Tamilnadu, India
e-mail: ethandapani@yahoo.co.in

Abstract. The authors consider the difference equation

Δ² (r_n Δ² y_n) ± q_n f(y_n) = Q_n; n = 1,2,3,... (*)

where r_n > 0, q_n > 0, for all n ≥ 1 and f : R → R is continuous such that uf(u) > 0 for u ≠ 0. Dividing the solutions of (*) into several classes for the cases Q_n = 0 and Q_n ≠ 0, the authors obtain conditions for the existence / nonexistence of solutions of (*) in these classes. Examples are inserted to illustrate the results.

2000 Mathematics Subject Classification. 39A10.

Key words and phrases. Difference equation, asymptotic behavior, nonoscillatory.

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