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