OSCILLATION OF A CLASS OF NONLINEAR DIFFERENCE EQUATIONS OF SECOND ORDER WITH OSCILLATING COEFFICIENTS

Year 2015, Volume: 3 Issue: 2, 211 - 218, 01.10.2015

Mustafa Kemal Yıldız

Abstract

In this paper, we study asymptotic behaviour of solutions of the following second-order di erence equation:
 a(n)
 x(n)+r(n)F(x(n􀀀))  +p(n)G(x(n 􀀀 ))􀀀q(n)G(x(n 􀀀 )) = s(n); where n 2 N0 := N [ f0g, fr(n)gn2N0 and fs(n)gn2N0 are sequences of real numbers, fp(n)gn2N0 and fq(n)gn2N0 are nonnegative sequences of real numbers, fa(n)gn2N0 is positive, ; ;   0 are integers and F;G are continuous functions satisfying the usual sign condition; i.e., F(u)=u;G(u)=u > 0 for u 2 Rnf0g. Various ranges of the sequence fr(n)gn2N0 are considered, and illustrating examples are provided to show applicability of the results.

Keywords

Asymptotic behaviour, neutral di erence equations, oscillating coecients, positive and negative coecients, second-order

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