Glasnik Matematicki, Vol. 33, No.2 (1998), 223-238.

OSCILLATION AND NONOSCILLATION OF QUASILINEAR DIFFERENCE EQUATIONS OF SECOND ORDER

E. Thandapani and L. Ramuppillai

Department of Mathematics, Madras University P.G. Centre, Salem - 636 011, Tamil Nadu, India


Abstract.   In this paper the authors establish conditions for the oscillatory and nonoscillatory behavior of solutions of second order quasilinear difference equations

Δ(an -1yn -1|α-1 Δyn -1) + qn f(yn) = 0

and

Δ(an -1yn -1|α-1 Δyn -1) + qn f(yn) = 0

when {qn}, {an} and the function f satisfy different type of conditions. Examples are inserted to illustrate our results.

1991 Mathematics Subject Classification.   39A10.

Key words and phrases.   Quasilinear difference equations, nonoscillatory solution, oscillation.


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