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

https://izlik.org/JA66WX36RW

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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