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 (rn Δ2 yn) ± qn f(yn) = Qn;     n = 1,2,3,...         (*)

where rn > 0, qn > 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 Qn = 0 and Qn 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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