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Dergiler / Konuralp Journal of Mathematics / 2015 / Cilt: 3 - Sayı: 2

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

Mustafa Kemal YILDIZ
Sayfa
211–218
Yayın Tarihi
2015-10-01
DOI
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Various ranges of the sequence fr(n)gn2N0 are considered, and illustrating examples are provided to show applicability of the results.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Various ranges of the sequence fr(n)gn2N0 are considered, and illustrating examples are provided to show applicability of the results.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Asymptotic behaviour · neutral di erence equations · oscillating coecients

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.

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Bu Makaleye Atıf Yap

YILDIZ, M. K. (2015). OSCILLATION OF A CLASS OF NONLINEAR DIFFERENCE EQUATIONS OF SECOND ORDER WITH OSCILLATING COEFFICIENTS. Konuralp Journal of Mathematics, Cilt: 3 - Sayı: 2, 211–218. https://ajindex.com/articles/786731

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Kaynakça (8)

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