Mustafa Fahri AKTAS, Ağacık ZAFER, Aydın TİRYAK

6593

Oscillation of third-order nonlinear delay difference equations

Third-order nonlinear difference equations of the form D (cnD (dnD xn))+pnD xn+1+qnf(xn-s)=0, n\geq n0 are considered. Here, {cn}, {dn}, {pn}, and {qn} are sequences of positive real numbers for n0 \in N, f is a continuous function such that f(u) /u\geq K > 0 for u \neq 0. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results.
Anahtar Kelimeler:

Difference equation, Delay, Third order, Oscillation, Nonoscillation, Riccati transformation

Oscillation of third-order nonlinear delay difference equations

Third-order nonlinear difference equations of the form D (cnD (dnD xn))+pnD xn+1+qnf(xn-s)=0, n\geq n0 are considered. Here, {cn}, {dn}, {pn}, and {qn} are sequences of positive real numbers for n0 \in N, f is a continuous function such that f(u) /u\geq K > 0 for u \neq 0. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results.
Keywords:

Difference equation, Delay, Third order, Oscillation, Nonoscillation, Riccati transformation,

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  • Corollary 3.2 Assume that all the assumptions of Theorem 3.5 hold, except that the condition (3.21) is replaced by lim sup m→∞Hm,m0 Kq− p2ρnd −σR d2 n+1 =∞ for every m ≥ n0, lim sup m→∞Hm,m A n=m0 ≥ n0. Then, every solution{xn} of eq. (1.1) is either oscillatory or limxn= 0 . n→∞
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
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