On the qualitative study of the nonlinear difference equation ...[wzór]

• Autorzy: Zayed E. M. E. , El-Moneam M. A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the global behavior of the following non-linear difference equation ...[wzór] where the coefficients α, β, y, p Є (0,∞) and σ, τ Є N and the initial conditions x_-x, x₀ x_-ω are arbitrary positive real numbers, where ω = max {σ, τ}.

Słowa kluczowe

EN

difference equations; prime period two solution; boundedness character; semi-cycle analysis; locally asymptotically stable; global stability

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2013
• Tom: Nr 50
• Strony: 137--147
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Zayed E. M. E.

• Mathematics Department Faculty of Science Zagazig University Zagazig, Egypt

autor

El-Moneam M. A.

• Mathematics Department Faculty of Science Zagazig University Zagazig, Egypt
• Mathematics Department Faculty of Science and Arts Jazan University Farasan, Jazan, Kingdom of Saudi Arabia

Bibliografia

• [1] Aboutaleb M.T., El-Sayed M.A., Hamza A.E., Stability of the recursive sequence xn+1= (α- βxn ) / (у + xn-1), J. Math. Anal. Appl., 261(2001), 126-133.
• [2] Agarwal R., Difference Equations and Inequalities. Theory, Methods and Applications, Marcel Dekker Inc, New York, 1992.
• [3] Elabbasy E.M., El-Metwally H., Elsayed E.M., On the difference equation xn+1= (axn-1+ βxn-k) / (Axn-l+ Bxn-k), Acta Mathematica Vietnamica, 33(1)(2008), 85-94.
• [4] Elabbasy E.M., El-Metwally H., Elsayed E.M., On the difference equation xn+1= axn- bxn / (cxn - dxn-1) Advances in Difference Equations, Volume 2006, Article ID 82579, pages 1-10, doi: 10.1155/2006/82579.
• [5] El- Metwally H., Grove E.A., Ladas G., A global convergence result with applications to periodic solutions, J. Math. Anal. Appl., 245(2000), 161-170.
• [6] El-Morshedy H.A., New explicit global asymptotic stability criteria for higher order difference equations, J. Math. Anal. Appl., 336(2007), 262-276.
• [7] Kocic V.L., Ladas G., Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht, 1993.
• [8] Grove E.A., Ladas G., Periodicities in nonlinear difference equations, Vol.4, Chapman & Hall / CRC, 2005.
• [9] EL-Owaidy H.M., Ahmed A.M., Youssef A.M., The dynamics of the recursive sequence xn+1= …[wzór] , Appl. Math. Letters, 18(2005), 1013-1018.
• [10] Kulenovic M.R.S., Ladas G., Dynamics of second order rational difference equations with open problems and conjectures, Chapman & Hall / CRC, Florida, 2001.
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• [12] Saleh M., Abu-Baha S., Dynamics of a higher order rational difference equation, Appl. Math. Comput., 181(2006), 84-102.
• [13] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = (D + axn + βxn-1 + yxn-2)/(Axn + Bxn-1 + Cxn-2), Comm. Appl. Nonlinear Analysis, 12(2005), 15-28.
• [14] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = (αxn + βxn-1 + yxn-2 + δxn-3) / (Axn + Bxn-1 + Cxn-2 + Dxn-3), J. Appl. Math. & Computing, 22(2006), 247-262.
• [15] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = …[wzór], Mathematica Bohemica, 133(3)(2008), 225-239.
• [16] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = …[wzór],Int. J. Math. & Math. Sci, Volume 2007, Article ID 23618, 12 pages, doi: 10.1155/2007/23618.
• [17] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = axn- bxn / (cxn – dxn-k), Comm. Appl. Nonlinear Analysis, 15(2008), 47-57.
• [18] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = (α+βxn-k) / (y-xn), J. Appl. Math. & Computing, 31(2009), 229-237.
• [19] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = Axn + (βxn + yxn-k)/(Cxn + Dxn-k), Comm. Appl. Nonlinear Analysis, 16(2009), 91-106.
• [20] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = yxn-k + (axn + bxn-k) / (cxn – dxn-k), Bulletin of the Iranian Math- ematical Society, 36(2010), 103-115.
• [21] Zayed E.M.E., El-Moneam M.A., On the rational recursive two sequences xn+1 = axn-k + bxn-k/(cxn + δdxn-k), Acta Math. Vietnamica, 35(2010), 355-369.
• [22] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1= Axn + Bxn-k + (βxn + yxn-k)/(Cxn + Dxn-k), Acta Appl. Math., 111(2010), 287-301.
• [23] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1 = (α0xn + α1xn-l + α2xn-k) / (β0xn + β1xn-l + β2n-k), Mathematica Bohemica, 135(2010), 319-336.
• [24] Zayed E.M.E., El-Moneam M.A., On the rational recursive sequence xn+1= (A + αoxn + α1xn-σ)/(B + β0xn + β1xn-τ), Acta Math. Vietnamica, 36(2011), 73-87.